Pike suffered injuries on a cadet vessel that was an "old Class J Starship" in "The Menagerie". That would indicate there must be at least one other class of starship other than the one the Enterprise belongs to. Well unless the Enterprise was also an "old class J" which I doubt.
I think Class J is just Starfleet slang for "junk."
So it could be a ship much like the Enterprise, but older and going out of commission.
Like Mudd's Class J as well
Anyway it still means that even back then they were thinking of more than one class or flavor of starship
. The Enterprise and her specific "Starship Class" starships had 12 active but there was room for other starships to exist as well.