Was Kirk reduced in rank to Captain for Star Trek the motion picture or was he addressed as Captain as head of the ship?

In Star Trek the motion Picture, it is established that Kirk is a rear admiral. However, he is addressed as Captain on the enterprise. Was this done because the heads of all vessels are traditionally addressed as captain?

Answer

At the start of the movie, Kirk's rank insignia is a gold leaf, showing he's an Admiral. When the Enterprise is underway, he's in a new uniform with the three strips on the sleeve cuff, a solid strip on the top and botton, with the middle strip interrupted. This is the Starfleet insignia for the rank of Captain.

At that point former Captain Decker has two solid stripes on his uniform, showing the rank of Commander. This is emphasized when Lt. Ilia first sees him and is puzzled and asks, "Commander Decker?"

So Kirk is a Captain by rank, as well as by title as the captain of the vessel.

It may or may not be worth noting that earlier, Decker has two stripes on his more formal uniform (I don't know if that was a dress uniform or not). It's also possible the shoulder insignia might differ from the sleeve insignia.

In the book, written by Gene Roddenberry, there's also a few lines that weren't in the movie in the scene in Engineering where Kirk tells Decker he's relieved of command. Kirk says:

You'll stay aboard as executive officer . . . a temporary grade reduction to commander.

This verifies that, for whatever reason, Decker could not remain in the rank of captain, which would make sense if Kirk's rank was reduced to Captain as well for the mission.

(Remember, the script for this came from the two hour pilot for Star Trek: Phase II and the original intent was to justify reuniting the old crew members and start a 2nd five year mission, where Kirk would be the captain and Decker would be the X.O. Even with a transfer to film, the idea of setting up another five year mission was still seeping through the final production of the movie.