The sources are not contradictory.
The time period being considered needs to be understood.
Heritage is going back to about 1982 (except for one earlier case from 1948 as Antlersoft and Nat point out!). For example:
In 1982, 27 individuals participated in an illegal scheme to boost
Honolulu voter registrations for candidate Ross Segawa. Segawa
was convicted on 10 counts of election fraud, criminal solicitation,
and evidence tampering. Segawa served a year in prison and was
expelled from law school. State Sen. Clifford Uwaine was convicted
of conspiring to illegally register voters and served three months in
jail; and Debra Kawaoka, an aide to Uwaine who also played a part
in the false registration, served numerous weekends in prison. Brian
Minaai and the other students each pleaded guilty to a misdemeanor.
A DOJ investigation of the Illinois election in 1982 estimated that
100,000 fraudulent ballots were cast in the gubernatorial primary.
The investigation was tipped off by a party worker from Chicago’s
39th Ward who was upset by his precinct captain’s broken promise
to award him a city job for his participation in the vote fraud
scheme. The conspirators cast ballots for people who were elderly
and disabled. The investigation resulted in 63 individuals being
convicted, the largest voter fraud case in DOJ history.
Vander Beatty, a former New York state senator, was convicted
of multiple criminal charges, including forgery and conspiracy,
in relation to election fraud. He led others in a scheme to forge
hundreds of voter registration cards to challenge the result of the
1982 congressional primary that he lost. He was sentenced to 16
months in prison and fined $5,000.
The categories of fraud need to be considered.
Heritage is considering many types of fraud. Specifically:
IMPERSONATION FRAUD AT THE POLLS: Voting in the name
of other legitimate voters and voters who have died, moved away, or
lost their right to vote because they are felons, but remain registered.
FALSE REGISTRATIONS: Voting under fraudulent voter
registrations that either use a phony name and a real or fake address
or claim residence in a particular jurisdiction where the registered
voter does not actually live and is not entitled to vote.
DUPLICATE VOTING: Registering in multiple locations and voting
in the same election in more than one jurisdiction or state.
FRAUDULENT USE OF ABSENTEE BALLOTS: Requesting
absentee ballots and voting without the knowledge of the actual
voter; or obtaining the absentee ballot from a voter and either filling
it in directly and forging the voter’s signature or illegally telling the
voter who to vote for.
BUYING VOTES: Paying voters to cast either an in-person or
absentee ballot for a particular candidate.
ILLEGAL “ASSISTANCE” AT THE POLLS: Forcing or
intimidating voters—particularly the elderly, disabled, illiterate, and
those for whom English is a second language—to vote for particular
candidates while supposedly providing them with “assistance.”
INELIGIBLE VOTING: Illegal registration and voting by individuals
who are not U.S. citizens, are convicted felons, or are otherwise not
eligible to vote.
ALTERING THE VOTE COUNT: Changing the actual vote
count either in a precinct or at the central location where votes
BALLOT PETITION FRAUD: Forging the signatures of registered
voters on the ballot petitions that must be filed with election officials
in some states for a candidate or issue to be listed on the official ballot.
For comparison, the News21 source (2012) relied upon by Politifact says:
The nation has 2,068 cases of alleged election fraud since 2000. By category, Unknown had the highest percentage of accused at 31 percent (645 cases), followed by Voters at 31 percent (633 cases). The most prevalent fraud was Absentee Ballot Fraud at 24 percent (491 cases). The status of most cases was Pleaded at 27 percent (558 cases).
So, while Politifact may portray the News21 source differently, its database contains more cases than Heritage in a shorter period of time, and includes 648 case where someone pleaded guilty or was otherwise convicted, plus 213 consent orders, in the 2000-2012 time period, plus additional cases of pending or unknown outcome.
Similarly, the list of 31 cases from Professor Justin Levitt is from 2000 to 2014, and is limited only to:
Credible allegations of potential fraud since 2000 that might have been prevented by a rule requiring ID at the polls