The idea of a pardon is exactly that: it erases the record of the crime/conviction.
I think you are thinking of a commutation. That ends the punishment while not absolving the person of the crime.
So the January 6th criminals who got pardons no longer have a criminal record (on this count at least). The 14 people who were only granted commutations are still counted as felons.
I must have read it incorrectly:
https://www.justice.gov/sites/default/files/olc/opinions/200...
> As these opinions confirm, a presidential pardon removes, either conditionally or unconditionally, the punitive legal consequences that would otherwise flow from conviction for the pardoned offense. A pardon, however, does not erase the conviction as a historical fact or justify the fiction that the pardoned individual did not engage in criminal conduct. A pardon, therefore, does not by its own force expunge judicial or administrative records of the conviction or underlying offense.