Looks like the AMT kit to me.
The desk model in "Booby Trap" was, in fact, a test shot of the kit from AMT/Ertl, before any of the surface detailing was added. We got a box of smooth styrene model parts in the mail, assembled the ship, and mounted it on a lucite stand built by the prop shop. As I recall, it had no decals, just a basic paint job.
As for the Enterprise in the shot with the other ship, I haven't a clue what that was.