I don't see the distinction. The Admiral of France was an office same as the Grand Seneschal or Constable. The title of Captain General of the Sea in Venice was granted by the Great Council of Venice, and wasn't a rank in the modern sense, if that's what you mean, even if more experienced sailors were usually chosen for the office. I don't see how that's different from other crown/state officers.
The book I linked, War at Sea in the Middle Ages and the Renaissance, mentions admiral as an office in England, France, Zeeland, Castile, Aragon, and the Almohads (as amir al-bahr).