His actual rank depends on the size and importance of the ship. On my ship, the captain was actually a Commander in rank, and our 'commodore' was actually a full Captain in rank. This eliminated the potential confusion of having two "Captains" running around on the bridge. We called our Commanding officer "Captain", and our flag officer "Commodore". Moskva was a big ship, and a flagship, so she probably rated an actual Captain as a master.

Being a ship's captain is a full-time job, so if the ship had a flag officer on board, I suspect he was a full Admiral in rank. Of course, it varies from navy to navy, and over time in any one navy, but that's the general situation. In the case of the Moskva, its not clear if the master or any of the Flag or his staff were casualties, the Russians have not really released much information one way or the other. I believe its because it might reveal just how big a bite the Ukrainians took out of their command hierarchy.

In the US Navy, the 9 officer ranks are as follows. I have placed the equivalent Army ranks and formations alongside for comparison.

O1 Ensign - Second Lieutenant (Platoon)
O2 Lieutenant Junior Grade - Lieutenant (Platoon)
O3 Lieutenant - Captain (Company)
O4 Lieutenant Commander - Major (Battalion)
O5 Commander - Lieutenant Colonel (Brigade)
O6 Captain - Colonel (Brigade)
O7 Admiral - General (Division) (There are several grades of Admiral and General)

When I was discharged, My enlisted rank was E-5, or Petty Officer Second Class