I think they are technically separate categories, albeit ones that often overlap.
I think corruption is essentially about self-dealing, whereas "bad faith" is when one abuses legitimate processes or powers while insisting that it's not abuse. For example, McConnell blocking Garland was done in bad faith, as was his refusal to hold a vote on the border wall stuff based on his assertion that Trump wouldn't sign it. But neither was corrupt, exactly.
Trump has deliberately eroded the distinction that is supposed to exist between himself as a private citizen and as a public servant, because he intends to steal from the Presidency for his own private gain, and this necessarily brings the two categories much closer together than they've ever been with any other office-holder.