if you want to cite a significant enough on-screen precedent to realistically consider it any kind of rule or even a commonality, you have to go to the spinoffs.
Since we only ever saw one class of starship (or indeed any Starfleet vessel) in TOS, and never heard a class name of any sort mentioned, this is a given. TOS-R changed things somewhat by showing us the Antares
, a potential Starfleet design, and by offering a resolution at which the discerning home viewer could see "Constitution Class" and "Starship Class" being used on the props.
It's not really a question of making TOS match the spinoffs through rationalizations or assumptions, as there's nothing in TOS to match.
And yeah, there's no "J Class" in TOS. There's only a "Class J" of training or transport ships. However, ENT uses the expression "J Class" on both the episodes dealing with these Boomer ships.