Opening caveat: land-based Anti-submarine/Intel Naval Flight Officer (back seater ala Goose or Bob) talking.

Training, training, training. Navy and Marine Corps carrier pilots have to land back on the boat. So as Mojos said, they spend an inordinate amount of time practicing carrier landings. I am fully confident that the top flight AF pilots could be Naval Aviators with the same amount of training. In fact, I'm pretty sure there have been some AF pilots who have become carrier qualified flying the EA-18 Growler on exchange tours.

Second, why was the mission in TG: Maverick a Navy mission and not Air Force? Range. For this story (making some major assumptions here, but jive with the plot as I know it), it was easier to park a carrier within strike range than to launch a mission from the closest friendly air base. Pilots with a 20-100 mile ingress "from the sea" should be more on their game than those that have to make a xxx or xxxx mile ingress with the requisite in-flight refueling stints (but having never done something like that, I stand ready to be corrected).

Third, the movie is a subsidized Navy recruiting movie. Air Force has the Iron Eagle franchise for it's recruiting purposes. 😉