Who knows? The 'captain' stuff may have all been in Kirk's head and he was officially an Admiral throughout TMP.
It would be odd for him to shift to the uniform of a grade that is only in his head. It is usually against regulations to wear the uniform of a grade one does not hold.
'Captain' is the customary title for someone in command, and we know from TOS, that officers above Captain can serve as starship commanders.
They're not called "captain," though.
During the course of the 20th century you have the O-7 rank being first a Rear Admiral 1st half, then Commodore, then Rear Admiral 1st half again. The O-8 rank was Rear Admiral 2nd half, then just Rear Admiral during WWII, then Rear Admiral 2nd half again. How that rank was displayed changed. Up through the mid 1980's all Rear Admirals wore 2 stars and the same stripes regardless of whether they were O-7 or O-8.
Not exactly; from 1899 to 1943 there was no one-star rank in the US Navy. Promotion was from captain to two-star rear admiral, equivalent to a major general. The pay rate would be the same as a brigadier general (what we now call pay grade O-7), however, until the rear admiral was in the top half of the seniority list, at which point he would get O-8 pay. In April 1943 the one-star rank of commodore was revived for temporary wartime-only promotions,
so in the latter part of WW2 both commodores and rear admirals (lower half) got O-7 pay.
Correction: I remembered wrong, commodores in WW2 received pay of the "6th pay period," the same as navy captain.
After the war the commodores who stayed in the navy reverted to their permanent rank, usually captain.
Up through the mid 1980's all Rear Admirals wore 2 stars and the same stripes regardless of whether they were O-7 or O-8. After briefly reviving the rank of Commodore (only 1 person briefly held that rank) the Navy changed the display of rank so that while O-7 and O-8 are both called Rear Admirals, O-7 wears 1 star and O-8 wears 2 stars to match the Army, Air Force, and Marines.
The 1980 Defense Officer Personnel Management Act created the 1-star grade of "commodore admiral" in the navy. The 1982 Defense Authorization Act (passed in 1981) changed the title to "commodore." Because of implementation provisions of the 1980 law, "commodore admiral" was rarely used in the short time it was authorized and officers were not listed under that grade in the Navy Register. The 1983 Navy Register listed 38 commodores: 30 line, 1 medical, 3 supply, 1 civil engineer, 1 dental, 1 medical service and 1 nurse. In 1984 there were 64 (Hey, Commodore 64!): 48 line commodores, 4 medical, 7 supply, 1 chaplain, 1 civil engineer, 1 dental, 1 medical service and 1 nurse. The 1986 Defense Authorization Act (passed in 1985) changed the grade to "rear admiral (lower half)," though in general practice 1- and 2-stars are both called simply "rear admiral".