Flight sims are games that try to simulate the real controls of an airplane. They often have complex controls and a high learning curve, but are rewarding once you figure them out.
Steel Diver was actually born out of Miyamoto's desire to create a flight sim, although he ended up doing a submarine because the speed of it would allow for an easier learning curve.
Pilotwings is not a flight "sim" because it does not simulate the real controls of an airplane. It could be categorized as a flight "action" game.
Nintendogs is considered a sim only in the same manner as The Sims or Simcity. I've always considered those strategy games, but everyone calls them sims for some reason.