Well, a Commodore is the same thing as a Rear Admiral, Lower Class. Most likely between TOS and TMP they just got rid of the Commodore designation and renamed it Rear Admiral, Lower Rank (just calling it Rear Admiral though).
I always figured Kirk was a Lower Rear Admiral (that's a heckuva name, lol) in TMP. The equivalent of a 1-Star Brigadier, since it'd only been two years since his mission with the Enterprise ended.
It's believable that there would be Commodores/1-Star Admiral in command of important Starship missions or Flotillas. Decker may have had other ships under his command but was on his own with the Constellation for whatever reason.
"Fleet Captain" I figured was an honorary/temporary rank made for Senior Captains who hadn't gotten a full-on promotion to Commodore/Rear Admiral yet.