Ah, the never ending question; Is a Captain always the Master, or the Master always a Captain?? To add to the confusion; we have Master Mariners and we have Skippers.
What defines all these titles? The answer may depend on whether it is a ship or boat you are talking about? It may also depend on the nationality of the person, and/or the vessel he/she is serving on.
But that raise the question of what is the difference between a ship and a boat?? And what in the h*ll is then a vessel?
Interesting topics, but may need to be taken up in a different thread?
To me the Master is the person entrusted by the owner and flag state authority as in full and overall command and authority on board on their behalf. There can only be one such person on board at any one time.
Whether he is also called Captain, or Skipper, and whether he is also a Master Mariner will largely depend on the type, size and trade of the ship/boat/vessel. (To some extent also what grade of license he/she is holding)
Captain is also a title given to a Master Mariner who has been in command of ships, which may be retained even after leaving that position. (Some do, some don't)