Originally posted by nuclear1
That would probably be a Vasudan mission. Who cares about Vasudan genders? 
First person to say "other Vasudans" or any other Vasudan sex joke gets a beating.
I do. I'd kinda like to know what gender adjective I should use in referring to them.
I suspect that you're seeing the ship's captain, although with destroyers it might be the Air Boss or the CAG.
An admiral is typically in overall command of a task force, but does not tactically direct the ship he is onboard: the captain fights the ship, the admiral directs the overall battle.
Since we rarely have more then one friendly capital craft on the battlefield, tactical command of the fighters would devolve upon its commander under most circumstances. On the other hand, guessing somewhat now, full captains would command destroyers or installations, commanders corvettes, lieutenant commanders cruisers, so there are situations in which a fighter pilot might outrank a cruiser commander. (You can give commands to the GTC Fortune in the mission during which you blockade the Knossos.)
Obviously GTVA ships would have a captain and an executive officer. The only other posistion that can be confirmed from the evidence available is the weapons officer, known colloquially as "Guns" (or at least they used to be; in the modern USN that position is referred to as "Weps"). Reference "Surrender, Belisaurius!" and the Psamptik saying "Guns, power up photon beam cannon. Commence plasma core insertion."