There's control surface flutter (which, technically isn't actually called "flutter", but we all call it flutter anyway)

And there's flutter of the entire structure, the whole wing or stab fluttering or flexing due to the aerodynamic loads on it.

Lots of causes for both, and lots of things to do to try to stop it. And yes, it's nasty. I stripped an aileron servo while testing out a new combat design last season. I went from flying fine to having 0 aileron control in an instant, and it was a fairly shallow dive that did it.