A private ship has no admiral aboard. The older use of "stag ship" discussed here refers to that status, while a later usage describes an all-male ship. The command analogy is a sergeant accustomed to running his own squad who now has an officer to answer to.
Notable Point · 1:56:57-1:57:30
Private ships and the changing meaning of stag ship
A brief naval command analogy distinguishes a ship without an admiral aboard from a later, different use of the term stag ship.