I’m no expert, but from the little I know I would guess that one is more “what is possible for me to do” (what courses of action are available) and the other is more “what am I able to do” (what’s within my skillset). I couldn’t tell you which one is which, though.
Oh. Even if derailing a bit from my usual studies, I rather like these little subtleties.
So they are pretty much the same. But there is that little nuance of やれる to be able to start doing something at least at first.
And 出来る carrying that certainty that you will actually pull it off.
It is, but calling やる simple the “more casual version of する” is one of those obnoxious things that won’t go away. There are definitely times when やる is either the only option, or the preferred option.