A commutation of sentence reduces a sentence, either totally or partially, that is then being served, but it does not change the fact of conviction, imply innocence, or remove civil disabilities that apply to the convicted person as a result of the criminal conviction.
A pardon is an expression of the President’s forgiveness and ordinarily is granted in recognition of the applicant’s acceptance of responsibility for the crime and established good conduct for a significant period of time after conviction or completion of sentence. It does not signify innocence. It does, however, remove civil disabilities – e.g., restrictions on the right to vote, hold state or local office, or sit on a jury – imposed because of the conviction for which pardon is sought, and should lessen the stigma arising from the conviction.
https://www.justice.gov/pardon/frequently-asked-questions-concerning-executive-clemency