post-ST2, future in-universe historians would label both variations "Constitution-class" regardless of the "Enterprise class" label of TWOK and "Starship class" of the bridge sign. I don't have an issue with that and gives it a real-world flavor.
I rationalize both of those bits like this:
- The Enterprise
-class designation refers to the simulator itself, not the ship. Either the simulator was made to resemble the Enterprise
, or it was intended for cadets who would one day be posted TO the Enterprise
- "Starship class" clearly doesn't make sense (if taken literally, it would require the existence of a "USS Starship
"). Clearly the sign should have said Starship TYPE, not Starship CLASS.