To be perfectly honest, with the way armor combat is actually conducted, I personally don't think they do overlap.
Granted, you need the reaction speeds and physical finesse but like piloting a fighter, a lot of it is actually a skill of its very own.
For example, hostile environment behavior (gravity well events, massive temperature shifts, hazardous obstacles, etc) aren't covered in general combat training. Neither are say BVR (Beyond Visual/Optic Range Combat), dogfighting (a common occurrence for many air based armors and a very useful skill to have) or the kind of in-depth knowledge like how armor users behave differently and how you can exploit the flaws of enemy training.