A false dichotomy and and the Constitution makes no such distinction.
Usually crimes committed while in office have nothing to do with the ascribed duties of the officer.
It is up to Congress to impeach and convict such an official while he is in office (Art. 1, Sec. 3, Cl. 7).
You’re combining impeachment by Congress - a political process - with judicial processes
Within the judicial process there’s convicting a president for doing things that while illegal are done for the advantage of the people versus doing illegal things for personal power
So no
Then was the guy even legitimately president.