Types of magic correspond to the way you think, your personality, your mental strength, etc. Regardless, if you train in any kind of magic extensively, then you can use it. Developing skills for it takes time though.
Magic isn't big and flashy, like bending would be (because honestly, a world where people can manipulate matter like that would be sent into anarchy by mass collateral damage) impractical.
I was thinking something more along the lines of Earthsea. Mages have their own specialties, and their sort of magic is usually based on years and years of training and continued usage of magic and an extensive knowledge in true names with specific entities. To be gifted in multiple branches is a feat on its own. To be proficient in all branches is so rare that people exhibiting those abilities are often scouted out and trained intensively to use those abilities with a lot of judiciously.
Likewise, with the mages here, they have to be able to learn how to feel specific entities and gain control over them, as well as calling forth similar entities from themselves. It isn't without intense practice that this can be achieved, and so even people with the gifts of magic may never reach their full potential without that type of training.
There are other ways to use the magic sense, such as feeling people's strengths, lifespans, conditions, and so forth, and there are ways to sense and control pieces of space and time to cast illusions, as well as ways to control the body so as to change it. Of course, fields like these are very obscure, as attempts to change too many things result in failure, such as time travelers always ending up a second, day, month, or year ahead of their own instead of going back, or lost vocal chords from too great a change, or cancer by trying to increase regeneration.
So magic is a very tricky thing that not many people use, and the few who do use it almost always take care of how far they can go with it before losing control.
