While the rank (if that's what it is) was mentioned twice in Star Trek, it was only mentioned in one episode...
In the opening scene of "The Menagerie", Kirk explains his presence with an expository line:
"Mr. Spock received a starbase transmission, a message from the former commander of the Enterprise, Fleet Captain Pike, urgently requesting that we divert here."
Soon thereafter, Commodore Mendez asks Kirk if he has met Pike before, and Kirk responds:
"When he was promoted to Fleet Captain".
Pike's rank is not mentioned after that. No other episode returns to the concept of Fleet Captain or suggests that somebody else would ever have held that rank.
To be sure, in "Whom Gods Destroy", Captain Garth is twice addressed as "starship fleet Captain". But that's in obvious reference to his elite status as a Captain in the starship fleet (and with respect to his related great responsibilities), not to his specific rank.
I personally prefer to think that since the universe is full of captains of all sorts, Starfleet Captains sometimes wish to stand apart. That is, Captain Christopher Pike, holding O-6 rank in Starfleet, would wish to be distinguished from captain Leo Walsh, holding no rank whatsoever while commanding his own freighter, but also from Commander Ramart, holding O-5 rank in Starfleet while captaining the
Antares. And the formal way to do that would be to call Pike "Fleet Captain" rather than just "Captain".
Why would Pike be a "special case"? I'm postulating that he had plenty of captaining experience before reaching the O-6 rank. He'd be promoted from O-5 Commander to O-6 Captain (with Kirk watching) but he'd all the time be captain of some starship or another - indeed, by his sleeve stripes, he'd already been captain of the
Enterprise while an O-4 Lieutenant...
To avoid confusion between Pike's rank and position, Kirk would thus emphasize the former by adding the seldom used specifier "Fleet". Kirk could have applied the same specifer to himself if he wished, or addressed Mendez as "Fleet Commodore" (perhaps to distinguish him from a convoy commodore or from a civilian with the title Commodore), but there was no corresponding need for that at the time.
Complex? Perhaps. But if it removes from the Star Trek universe an irritating detail that only exists in a single episode for the duration of about one minute, it's worth it...
Timo Saloniemi