I think the biggest differences between a flight simulator and an FPS is a flight simulator is way closer to the real thing than an FPS.
Flying a plane is largely sitting a seat, moving a control stick and other switches (simulated by the keyboard, or for you hard core simulators, actual gauges and switches.) Want the plane to turn left? Move the stick left. Use the foot pedals to control the vertical flaps, While I would never want to fly with a “sim only” pilot, one could probably transition from PC to IRL at least half the time with proper practice.
There is NOTHING like real life in a FPS. Want to look left? You have to move your body holding a 7-8lb weapon left, not move a thumb. Want to load it? It is usually automatic, or you hit a button in the game. There is a multi-step process IRL that requires some fine motor skills. The red-dot or sights? They don’t hold anywhere near that still unless you’re prone or supported. Want to actually MOVE? You gotta actually use your feet and start breathing to get oxygen to your muscles. Want to fire it? Congrats, you now can’t hear anything because you didn’t have ear protection and it is going to get worse. The recoil may be simulated similar in some games, but the way you actually have to adjust to it IRL is way different.
Anyone who thinks an FPS is anything like IRL either is so young they think a cape might let them fly if they get a good jump, or has the Dunning-Kruger effect so bad that they think they can do anything.