I believe in Once that internal magic is something you have to have that “spark” for, and then you can learn it. So being magical is something that, barring access like the Dark One’s dagger, you have to be born with. But to really use it requires training (and if you don’t have obvious signs like Zelena, how would you know to be trained? So probably there are many born with the spark who never seek training).
Magic items can be used by anybody.
Some curses/items can grant magic abilities to the user. I highly suspect that the effects of knowing how to use magic are permanent, though, even if the curse is later lifted–I think we saw that with Cyrus in Wonderland. Perhaps once that spark is created, you never quite lose it, even if your powers are diminished once no longer under the curse.
Keeper of Belle's Gold magic, sand dollar, cloaks, purple FTL outfit, spell scroll, library key, copy of Romeo and Juliet, and cry-muffling pillow, Rumple's doll, overcoat, and strength, and The Timeline. My spreadsheet: https://drive.google.com/file/d/0B6r8CySCCWd9R0RUNm4xR3RhMEU/view?usp=sharing