In general, you have a particular unit like a ship or aircraft. That unit is part of a squadron. That squadron could be like an aircraft squadron, where there's a CO, or like a destroyer squadron, where you have a commodore. For aviation, each squadron belongs to a Type-wing which is responsible for the administrative control of the aircraft and squadrons. Fighters belong to a FITWING, HS or HSL belong to HSWING or HSLWING. Sometimes there is more than one wing for a specific type. For example, for HSL there's HSLWINGLANT and HSLWINGPAC (and before everyone jumps on me, yes, I know everybody has been renamed, but it's easier this way. Besides I can never remember the order of HEL, MAR, STRIKE, and whatever else they use). These wings are commanded by the "Commadore," which usually is an O-6.
These Type-wings are different from Carrier Air Wings, which take operational control of all the different kinds of aircraft that are part of a CAW. A CAW is run by the CAG, or Commander Air Group.
So, for the training squadrons, you have TRAWING 6, which is all the training aircraft at NASP (VT-4, VT-10, and VT-86). TRAWING 5 is at NASWF, and controls VT-2, 3, 6 and HT-8 and 18. TRAWING 4 is in Corpus, and so on. The exception here is that these wings control different types of aircraft (T-34, T-1, Saberliner, TH-57, T-44, TC-12, etc) w/ in their respective commands.
Hope that helps.
Bah, Pags beat me to it.