'CinC' Commander in Chief...normally only applies to the President.
Not necessarily. The term can also be used to refer to the commanding officer of a theatre of operations. For instance, the commanding officers of the U.S.'s Unified Combatant Commands
used to hold the title of "Commander-in-Chief, [UCC name] Command."
So it's entirely plausible that the commanding officer of the entire Federation Starfleet could hold the title of Commander-in-Chief of Starfleet, while the Federation President would presumably be the Commander-in-Chief of the entire UFP armed forces.