In the 1990s, there were at least 3 separate shared universes for Star Trek games, each with their own unique recurring original characters, ship designs, and species.
MicroProse:
Interplay:
Activision:
Interestingly, Starfleet Command I & II were in the Interplay TOS-era shared universe, while Starfleet Command III was in the Activision TNG-era one.
A couple ship designs from both the Interplay-verse and the Activision-verse have shown up in Star Trek Online, notably the Federation fighters from Starfleet Command and Shattered Universe and the Federation carrier from Star Trek: Invasion.
Also Simon & Schuster produced a bunch of Star Trek games in that same era, but I don't think they had an ongoing storyline or recurring original characters/ships/factions between them like the other publishers did.