The Confederates had taken part in a rebellion against the US, so yes, they did commit an offence. As to Nixon, he was expected to be impeached and chose resignation instead. But I believe Ford bastardized the power of the pardon. Draft dodgers had committed a crime and would have been charged upon return to the US.
As the pardon power goes now, I believe is not how it is written nor exercised. JMHO and thanks for the examples.
If Hillary were to accept a pardon, she would be admitting guilt, as did those others who received pardons/amnesties.
Benton Becker negotiated the pardon deal with Nixon. Using the language of Burdick v. US, Nixon admitted legally to obstruction of justice. Becker describes how he gave Nixon a take-it-or-leave-it deal.
Leftist rage against Nixon was that he never groveled before the moral authority of the MSM. And Leftists conveniently do not cite Garland because it relies on original intent and common law.