It can absolutely be both (or all three—I take “being special” as distinct from “your own power”), in different mixes for different people.
I’m not sure about the “useful for personal purposes” part. A lot (but not all) fantasy wizards pay a fairly high social cost for their erudition, and it’s not clear that all that studying and experimenting helps them nearly as much as just getting rich and hiring an army would.
All that said, there’s a limit to what we should learn from fiction.
It can absolutely be both (or all three—I take “being special” as distinct from “your own power”), in different mixes for different people.
I’m not sure about the “useful for personal purposes” part. A lot (but not all) fantasy wizards pay a fairly high social cost for their erudition, and it’s not clear that all that studying and experimenting helps them nearly as much as just getting rich and hiring an army would.
All that said, there’s a limit to what we should learn from fiction.
people use magic for purposes you can’t use an army for XD