I think events went sorta like this-
1. When Jefferies came up with that "1701" number, he retconned a decision made purely on visibility as being indicative of the first ship built in the seventeenth group of starships. So, when conceived, Enterprise was the class vessel. At least to Jefferies.
2. Along comes "Doomsday Machine". For whatever reason- convenience, visibility, distinctiveness, etc- the ship scripted as being "Enterprise type" is numbered "1017" and named "Constellation". This is the first ship seen onscreen that looks like Enterprise.
3. Later, a graphic of an Enterprise ship's phaser is needed. Whoever puts the thing together remembers that they've established some ship as having a lower number than Enterprise, probably because the obvious problems with a "1017" number were discussed and still on his mind. He misremembers the lower numbered, "1017" ship Constellation as Constitution and puts that name on the graphic.
4. By the time Trimble is putting together her book, we have a Constellation with the lowest number, but a graphic hinting all these Enterprise-type ships are Constitution class. So we end up with fans making sense of the mess as Constitution being the prototype and class vessel (00), Enterprise being the first produced after the prototype (01), and Constellation being an older ship uprated to Constitution standards (1017).
5. Later, an attempt is made to make things right when TMP introduces the brand new, first of her type, rebuilt Enterprise. Probert, Cole and Kimble call this new class "Enterprise class" in an attempt to get back to what was originally intended back in 1964 and to recognize the entirely new nature of the design.
6. But even later, different artists try to "fix" the "mistakes" of the TWoK bridge simulator plaque and the TMP blueprints by identifying a ship looking like the rebuilt Enterprise as once again... Constitution class.
7. BUT this TMP-looking ship is ACTUALLY 1701-A. Some fans (like me) make sense of this new mess by saying that the rebuilt 1701 is Enterprise class but that 1701-A is Constitution class. Either because the class name was changed after the loss of 1701, or because 1701-A was an outwardly similar but inwardly different class.
8. In any event, if you want to go strictly by what was seen onscreen, the TOS Enterprise is "Constitution class" as established in later series, and "Star Ship Class" as established on the dedication plaque seen in the episodes. The TMP Enterprise is "Enterprise class" per the bridge simulator in TWoK, and the new 1701-A is "Constitution class" per the blueprints seen in ST VI. The only apparent contradiction is "Constitution" versus "Star Ship" class for the original ship. And that can easily be resolved by saying that "Star Ship" either represents a later, select subset of Constitution class ships (perhaps the 5YM ships?), or that "Star Ship" is an earlier designation, perhaps implying the ships were named for famous starships or indicating a broader "type" category as has been argued here. In any event, within the context of strictly TOS it is correct to call Enterprise a "Star Ship class" vessel. But within the broader context of the later series it is correct to also call her (and Defiant) "Constitution class" vessels.
