tl;dr:
The words "Hakenkreuz" and "swastika" describe one and the same symbol, one time in Sanskrit and English, one time in German. Some believe that this 'is' an ancient Germanic symbol, some that it 'is' an ancient Indic. Both these schools argue with archaeology and unbroken tradition, Both claim that this is inherited from a not merely spreading but 'conquering' Indo-European (Indo-Germanic, abbreviated: IE) conglomerate of 'ancestors', in this case until the 1940 popularly often called 'Aryans'. This shared similarity falls flat for the criterion of 'original invention', as there is ample 'prior art' thousands of years older than any proponent of these claims can account for and apparent 'independent invention' of older, and of non-Indo-European cultures for this simplistic symbol to be found virtually everywhere.
European nationalists and Hindu nationalists are therefore both wrong to at least come together in the claim "we (our ancestors) invented this", even if anyone should assert any unbroken tradition and continuity of cultures, which is also wrong in the first place.
The waning but never extinguished popularity of the hooked cross in Europe was over time largely re-interpreted as to be read as a variant of a Christian cross. Only through the reception of Indian and other 'Eastern' 'mysticisms'/religious ideas and linguistic as well as ethno-cultural studies in the 19th century, some Europeans thought this 'Indian reading' – and thus 'Aryan' – of the symbol would have preserved the 'original', or pre-Christian, reading of the ancient symbol.
The eventual Nazi-use of the symbol is therefore formed in reaction to the then 'newly found' Indian tradition and thus inseparable from the Indian variant reading. This is directly traceable through European mystics, 'Aryan' nationalists writing and usage. This political extremist right-wing reading of ultra-pan-Germanists and forgers of history became the dominating line of interpretation for this symbol in 1935, when it was made sole national flag of Germany. As the Hitler movement started in 1920 they enshrined with references to 'Eastern' meanings (and religions) this symbol as their own and through the popularity of Nazis and their iconography this is now what we look at: a universal symbol of the most simplistic design that in the West 'has' to be read as meaning much different things than in many other parts of the world. Only for the 'post'-1935 prescribed readings in the West did Hitler contribute much 'original work'.
The swastika Hitler inherited from his ideological völkisch progenitors is a universal symbol. The swastika as it came to be used under national-socialism is inseperable in its intellectual tradition of reading the symbol from the Indian variant of it. Without the Indian version and its contemporary influence in 19th century European nationalism, and a variety of other connected ideologies, the Nazi swastika is unthinkable.
That swastika was in use in the right-wing nationalist movements of the time for decades when Hitler selected it as a trademark sign for his party. Until then and some time later the symbol was still widely read as not specific to nazism, although this reading then came to dominate the interpretation.
The symbol is never mentioned to be of specifically 'Indian origin' by Hitler himself, neither in speeches nor in his book Mein Kampf. Nor is the monastery legend connected to Lambach. In his book he only makes a fleeting mention, that of all the proposals presented to him, many already including the swastika of some sorts, he as Führer selected the 'best one' and finalised it in terms of orient-ation, colour-scheme and proportions. It was his own, by sheer coincidence, as I am sure you will also believe…
The claim originating article therefore re-tells a lot of nazi myth and is "not true".
The Indian swastika and the Nazi swastika are identical symbols. That does not say that both mean the same things. Symbols are empty vessels to be filled by the expectations of the spectator. They could mean the same thing: symbol of right-wing hatred in 'White nations' or a 'Hindu nation'. Or just 'good luck'…
The swastika Hitler's party chose only came to prominence in nationalist thinking because it was known to be an ancient symbol of ancient India and the nationalist Europeans invented a tradition of 'white conquest' (or "Aryan expansion") that claimed this symbol would be proof of European identity and dominance, only that Europeans largely forgot it in the meantime and Indians preserved this abstract artifact in a much more widespread manner. The supposedly connecting dot being that Schliemann claimed to have excavated (in Asia!) the 'European' city of Troy where such symbols were found as well, rivaling Indian finds at the time in terms of 'boy, that's old'.
The claim that Hitler saw a variation of the swastika symbol in an Austrian abbey as a young boy is true.
But that he took this as inspiration for re-purposing a Christian symbol of a cross is a Nazi myth invented or ret-conned only long after Hitler came to power.
The symbolism in the monastery is clergical and thus Christian, as that one Benedictine abbot from the 19th century chose a non-right angle variant, meant as a Christian cross, as his personal heraldic symbol. While Hitler was deeply influenced by Catholicism and used its methods and doctrines atavistically, the whole goal of his enterprise was to root it in a 'more original' way, an older way, as 'older' was better. The pagan pre-Christian tradition of pre-Germanic peoples of this symbol has therefore precendence. The 'young Hitler got it from abbey' is a nazi lie.' (cf: Grossruck)
And not even an 'official nazi lie'. The swastika was in use in that nationalist scene long before Hitler joined any party, he never mentioned the connection to the abbey, and surely not as in 'want a Hakenkreuz just like in my childhood abbey', and local nazis in Lambach (Austria!) took the opportunity to paint a short-staying Hitler getting inspired as a 'city's great son' (after Anschluss in 1938!). Despite the symbols only vaguely matching, representing different things, Hitler ignoring that completely and the folk-etymology of a 'Hagn-Kreuz' giving rise to a Hitler's Hakenkreuz being ridiculously far-fetched and easily seen as completely ahistorical.
In 1883, however, an Austrian schoolmaster, the gymnasium professor Carl Penka, published a monograph that made the claim that the Indo-Europeans were indigenous to Europe and had expanded into the orient by conquest. This notion of indigeneity soon began to receive support from German academics and by the turn of the century had achieved some level of academic respectability. The early proponents of an Indo-European origin in Germany clearly fed off anthropological speculation; yet they were also obviously arguing a national question.
Very soon the connection between German, Germanic and Indo-European (the latter identity still to this day usually termed indogermanisch, i.e. Indo-Germanic, in German) was also to become a mainstay of völkisch thought too.
With the siting of the aryan homeland in the German north, the Aryan identity received new importance. Chamberlain, after all, had bound classical antiquity and ancient Germany together as chapters in an Aryan antiquity. He had used the term Aryan only in its anthropological sense (which is more clearly described as Nordic or Caucasian), but as the realization of the implications of Indo-European linguistics entered anthropological and archeological discourse in the later decades of the nineteenth century, the anthropological identity Aryan had become fused with the linguistic one. Aryan only properly designates the Indo-European peoples of India and Iran (and indeed the latter place-name derives from ‘aryan’). Yet when Schliemann discovered symbols identical to Hindu swastikas among his much-publicized discoveries at Troy, swastikas became the symbols of an occidental Aryan identity. The Greeks of Homer, no longer the mythical figures they had once seemed, now represented the oldest of occidental Indo-European cultures, one even as old as ancient India and Persia. As an occidental hallmark of Aryan culture, Schliemann’s swastika soon also came to penetrate völkisch literature: the connection between Aryan (Indo-Germanic) and Teuton (Germanic) had achieved a physical, concrete and easily recognizable symbol. Goblet d’Alviella’s study was also employed to show that although the swastika was widely known throughout the world’s cultures, the earliest examples of the symbol were attested only in central Europe. D’Alviella’s diagrammatic depiction of the distribution of swastikas in Europe and Asia became a mainstay of both academic and völkisch interpretations of the origin and nature of the swastika. The swastika became the symbol par excellence of the Aryan, or in anthropological terms, the white race.
By the 1920s swastika studies had developed a number of theories about the swastika and what were thought to be related prehistorical symbols: the circle, the circle-cross and the cross itself (which according to Montelius had been adopted by the church from prehistoric practice). The connection of the sun with these symbols also led to the notion of primitive aryan sun worship, a cult which in description was clearly monotheistic.
— Bernard Mees: "The science of the swastika", Central European University Press: Budapest, New York, 2008. 'The Origins of Ideographic Studies', p57. (Links added for convenience, LLC)
This 19th century academic opinion which was 'scientific' is now quite outdated.
The oldest civilisation using the swastika/Hakenkreuz in Europe wqs the pre- and non-Indo-European, old-European Danube or Vinça-culture (5700 BC). The proto Indo-European homeland may from 4000 BC be the 'point of origin' for Indo-Europeans, but while the absolute dating for that may be a bit unclear, it is not unclear that the early Indo-Europeans did not use anything archaeology could dig up that 'knows' this symbol. They 'learned it' from contact with that older civilisation.
Similar patterns can be seen for Finno-uralic peoples, Siberian, Chinese and Harappan culture. All used the symbol before Indo-Europeans 'made contact' with them, and then the latter adopted the symbol. As seen by Andronovo people (IE), Helladic migrants to Greece or Aryans in India.
(— Harald Haarmann: "Auf den Spuren der Indoeuropäer: Von den neolithischen Steppennomaden bis zu den frühen Hochkulturen", CH Beck: München, 2016. gBooks)
In Hitler's Mein Kampf we get a glimpse of how this committee work for choosing a brand played out:
Die Frage der neuen Flagge, d.h. ihr Aussehen, beschäftigte uns damals sehr stark. Es kamen von allen Seiten Vorschläge, die allerdings meist besser gemeint als gut gelungen waren.
[…]
Dennoch mußte ich die zahllosen Entwürfe, die damals aus den Kreisen der jungen Bewegung einliefen, und die meistens das Hakenkreuz in die alte Fahne hineingezeichnet hatten, ausnahmslos ablehnen. Ich selbst – als Führer – wollte nicht sofort mit meinem eigenen Entwurf an die Öffentlichkeit treten, da es ja möglich war, daß ein anderer einen ebenso guten oder vielleicht auch besseren bringen würde. Tatsächlich hat ein Zahnarzt aus Starnberg auch einen gar nicht schlechten Entwurf geliefert, der übrigens dem meinen ziemlich nahekam, nur den einen Fehler hatte, daß das Hakenkreuz mit gebogenen Haken in eine weiße Scheibe hineinkomponiert war.
Ich selbst hatte unterdes nach unzähligen Versuchen eine endgültige Form niedergelegt; eine Fahne aus rotem Grundtuch mit einer weißen Scheibe und in deren Mitte ein schwarzes Hakenkreuz. Nach langen Versuchen fand ich auch ein bestimmtes Verhältnis zwischen der Größe der Fahne und der Größe der weißen Scheibe sowie der Form und Stärke des Hakenkreuzes.
Und dabei ist es dann geblieben.
— (AH: "MK", 1925, p555–556. translation here)
Coincidentally, in this passage AH explicitly rejects a shape more closely resembling the monastery symbol than what we later saw on nazi flags.…
In this design finding stage for the brand we are looking at the years 1919-20. With the swastika being a well established völkisch and anti-semitic symbol we also find AH still struggling to choose 'the correct' version, in contrast to his fait accompli characterisation in Mein Kampf:
Before May 1920: "The sacred signs of the Germans(Teutons). One of these signs should be resurrected again by us."
— Rüdiger Sünner: "Schwarze Sonne. Entfesselung und Mißbrauch der Mythen in Nationalsozialismus und rechter Esoterik", Herder: Freiburg, Basel, Wien, 1999. (P177. Original in possession of the Bavarian Ministry of Finances.)
The direct connection between swastika using predecessor organisations in Germany and the NSDAP of Hitler — excluding the antecendent armed militants like Freikorps (example: Marienbrigade Erhardt) — was Friedrich Krohn, the infamous "dentist" from Mein Kampf:
Although the DAP and the Thule Society diverged in their views on ideology and action, there was a direct line of symbological succession between the two groups in the form of the swastika. Friedrich Krohn, a Thulean and a member of the Germanenorden since 1913, had earned the reputation of a DAP expert as a result of his collection of some 2,500 books on völkisch subjects for the use of party members. In May 1919 Krohn wrote a memorandum with the title 'Ist das Hakenkreuz als Symbol nationalsozialistischer Partei geeignet?' ['Is the swastika suitable as the symbol of the National Socialist Partv?'] in which he proposed the left-handed swastika (i.e.clockwise in common with those of the theosophists and the Germanenorden) as the symbol of the DAP. He evidently preferred the sign in this direction on account of its Buddhistical interpretation as a talisman of fortune and health, whereas its right-handed (i.e. anti-clockwise) counterpart betokened decline and death. (However, since most Listian swastikas and the device of the Thule Society had been right-handed, it is clear that there was no standard usage regarding the direction of the swastika in the völkisch tradition). Hitler actually favoured a right-handed, straight-armed swastika and prevailed upon Krohn in DAP committee discussions to revise his design. Krohn was responsible for the colour scheme of a black swastika in a white circle on a red background. At the foundation meeting of the local Starnberg group of the NSDAP on 20 May 1920, this swastika, originally proposed by Krohn and modified by Hitler, made its first public appearance as the flag of the new movement. It is therefore possible to trace the origin of the Nazi symbol back through the emblems of the Germanenorden and ultimately to Guido von List.
— Nicholas Goodrick-Clarke: "The Occult Roots of Nazism: Secret Aryan Cults and Their Influence on Nazi Ideology", I B Tauris: Londion, New York, p151, 2004.
— Malcolm Quinn: "The Swastika: Constructing the Symbol", Material Cultures, Routledge: London, New York, 1994.
— Thomas Wilson: "The Swastika. the Earliest Known Symbol and its Migrations; With Observations on the Migration of Certain Industries in Prehistoric Times", U.S. National museum, 1896. (various version on archive.org)
— Johann Grossruck: "Benediktinerstift Lambach im Dritten Reich 1938 –1945. Ein Kloster im Fokus von Hitlermythos und Hakenkreuzlegende", Wagner Verlag: Linz, 2011. (Esp p 151–174; review)
How 'the dentist' Krohn tried to seel the idea in his text reads:
Personally I may add in all modesty that I found the swastika (sun wheel) [(in German original: "Hakenkreuz", LLC)] in 1912 also on an old coat of arms of our family and therefore I am also personally very attached to this sign. Therefore I would like to ask especially my party friends of the DSP or the DAP and the Wälsungenorden / Thulegesellschaft to choose this victory sign as a symbol of our occidental defence and struggle of renewal, as our brave fighters against the Asian red hordes in the east in the Freikorps partly did use already. Sieg und Heil!
— own translation, quoted from: Sibylle Friedrike Hellerer: "Die NSDAP im Landkreis Starnberg. Von den Anhängen bis zur Konsolidierung der Macht (1919-1938)", Dissertation, Ludwig-Maximilians-Universität München, 2014. (PDF)
Net ressources:
— Peter Diem: "Die Entwicklung des Hakenkreuzes zum todbringenden Symbol des Nationalsozialismus", mirror
— Heraldik-Wiki: Swastika
The frame of this question is quite odd. A basic geometric shape when interpreted as a symbol of magical qualities that is found throughout all of history and across the globe does not carry any inherent meaning. This 'meaning' is solely attached to it by the viewer and thus one probably shouldn't say that this is an 'Indian symbol', or a 'nazi symbol'. It is much better fitting to describe this shape as 'is used by' Hindus or Nazis, as just two examples. This doesn't change the fact that in contemporary Western culture the association between swastika and nazism is almost congruent now, if not a relationship of identity. But as such, this invented tradition came late:
In 1891, when Michael Zmigrodski defined the swastika as the armorial shield of the Aryan race, his heraldic metaphor was apposite in several senses: the Aryan swastika was both the precursor heralding an absent or delayed referent meaning, and also its defensive shield. It was also heraldic insofar as the ‘tradition of the symbol’ and the repetition of the sign was a mimesis of racial lineage and pedigree. In this ‘heraldic’ form, the swastika itself does not ‘mean’, it produces meaning by announcing it on the one hand and obscuring it on the other.
(— Quinn)
It is bit of a cat and mouse game here: 19th century Europeans saw the Indic swastika and admired the oldness of that culture and liked this recognisable symbol. Then they found the same symbol and close relatives of it in their archaeological excavations 'closer to home' and sometimes even older than from India. They 're-discovered' the symbol as 'our own', despite it never fading completely from decorations or heraldry. Instead of assuming a parallel development of a simplistic structure, they wanted a single point of origin, an 'unbroken tradition' and concluded 'conquest' and domination from that. No matter how implausible and of course disregarding any evidence to the contrary.
In Nazi/European ideology, 'the Indic swastika is inherited from Aryan ancestors', not the other way around. Whether Hindus, stone-age people or Germanic peoples also used it is irrelevant, we see it in constant cultural appropriation…
That means in European heraldry, a swastika is not so rarae as many may believe now:
will not rehearse either the purported ancient origins of the swastika or the manifold contexts in which swastika-like devices are found. Like others who have written on the subject, I find, in any case, that such an approach fails comprehensively to mitigate the instinctive reaction the swastika now inspires in the West. On the contrary, the nineteenth-century antiquarian practice of spotting swastikas and building connections played a major part in the construction of what the swastika was to become.
— Clive Cheesman: "The Heralds’ Swastika", in: Fiona Robertson and Peter N. Lindfield (Eds): "The Display of Heraldry. The Heraldic Imagination in Arts and Culture", The Coat Of Arms Supplementary Volume No 1, The Heraldry Society: London, 2019.
By the time Hitler was born in 1889 and then afterwards, he could have seen that symbol in lots of places, like the aforementioned abbey. But there it was a Christian symbol. It was not so much Christian in Rudyard Kipling's books, on beer bottles from Carlsberg. And it was firmly established then to this Germanic/Aryan reading-thing through many writings, and respected artworks:
— Mårten Eskil Winge: "Thor's Fight with the Giants" (1872) (Referenced on Wikipedia: "Early Germanic culture" no less. Hint: the belt.)
Therefore, the claim that "Adolf Hilter probably never heard the word swastika" is quite the bogus one. The "Swastika" and "Hakenkreuz" are perfect synonyms, and one is the usual German translation for the other (the 'proper' German word being in dictionaries from at least the 18th century). Just that there are certain preferences around any particular usage:
This caveat was issued in 1880 by the philologist Max Müller in a letter to the archaeologist Heinrich Schliemann, then known throughout Europe as the excavator of Troy. In his letter, Müller warned Schliemann that he should be wary of confusing the word ‘swastika’ with an archaeological ‘found image’, and that to do so would sever the links between the symbol and tradition:
I do not like the use of the word Svastika outside India. It is a word of Indian origin, and has its history and definite meaning in India. I know the temptation is great to transfer names, with which we are familiar, to similar objects which come before us in the course of our researches. But it is a temptation which the true student ought to resist, except, it may be, for the sake of illustration. The mischief arising from the promiscuous use of technical terms is very great.
(— Quinnn, p1)