No, continental rocks are not the same as ocean floor.
Continents are mostly made up of minerals like granite, which are lighter than ocean floor minerals like basalt (sima, short for Silicon/Magnesium). Continental material is mostly sial (short for Silicon/Aluminium) which is lighter. Partially molten mantle material is pushed up at mid-ocean ridges, which then causes the tectonic plates (ocean plates) to move apart. As the mantle material is not fully molten, the composition of the melt is different from that of the mantle, which in turn is different from the continents.
As the continents are lighter they effectively float on the oceanic floor, and travel along with the spreading seafloor. There is abundant evidence for the movement of tectonic plates. The first discovery was the striped magnetism of the seafloor, caused by the effect of earth's reversing magnetic field on solidifying rock. Earthquakes are also far more prevalent at plate boundaries than elsewhere, and maps show quite clearly that earthquake follow the boundaries.
Continental movement has been measured directly with GPS satellites, and also by bouncing lasers off the reflectors that the Apollo astronauts left on the moon. Of course, conspiracy theorists may not believe those mirrors are actually there... At least they would have to admit that GPS works.
Continental drift does not necessarily mean that all the continents ever were joined together. However, there is a lot of evidence for that, too. Start with the way the continents fit together. There is also the distribution of related fossils across different continents (leading, for example, to marsupials in Australia and the Americas only), which would otherwise be very hard to explain. And, there is the fact that, if you join the continents together, geological features line up. Again it would be a funny coincidence if this happened without them having been joined while those features were formed.