Sort of.
A crime is a crime is a crime. It's illegal to use your Constitutionally-provided authority with "corrupt purpose". Firing a staffer isn't illegal. Firing a staffer in an attempt to stop an active investigation into a member of your campaign IS illegal.
It's just that if you're a sitting President, the remedy for that illegal activity is impeachment. (Also the way Impeachment of structured, you don't have to have met the strict legal definition of a crime. It's for "high crimes and misdemeanors", but Congress decides what was a crime, not the Judiciary)
Having said that, once a President is removed from office- they can face criminal charges. Remember, Gerald Ford pardoned Nixon immediately upon becoming President (that's why his approval ratings were so historically low) because he knew Nixon would face criminal charges for his conduct afterwards.