In FSX, the carriers are moving, and available in missions only, and is not available for general use. In FS2004 the carriers are statically placed at four locations around the world, and can be selected as locations like airports. There are three different aircraft to fly from the carriers:
AV8B Harrier II Plus (UK)
F-35 Lightning II/JSF (USA).
Rafale M (France)
Missions for FSX (only) with goals/rewards:
Joint mission training: fly the F-35 around a task force with all three carriers
HMS Illustrious training: bombing practice with US Navy & Marines at Cape Wrath
MiG Crisis: the US carrier task force is being approached by hostile MiG:s in the North Pacific, intercept and stop them
MiG Thunder 1/2/3: the French carrier is under attack off South America/in the Mediterranean/off the African coast
Plus 6 open-ended practice missions without goals: practice operations in Hawaii, Indian Ocean, Philippines, Suez Canal, New Orleans, and Panama Canal.