That's not correct, it's PIC when any time you are not taking dual instruction and you are flying the airplane and authorized to do so, such as when signed off to perfrom a cross country, also including a certain loophole which applies to flying as safety pilot for instrument students. Think about it this way: if you are doing your solo cross countries you do not have your private certificate yet, but you are flying alone is there no one acting as PIC onboard? I hope there is.

Another distinction to make is private pilot, commercial pilot, certified flight instructor, and airline transport pilot are certificates, whereas an instrument ticket, multiengine ticket, and type-ratings are ratings. Note that some ratings are not required to fly that airplane and some are. For example, any private pilot can hop in a C172 or a Piper Arrow and fly, but a private pilot cannot hop into a very light jet and fly that aircraft because it requires a type rating.

Some aviation credentials are handled as endorsements, such as the tailwheel, high performance, complex retractable, and high altitude endorsements.