There seem to be two basic types (at least, as far as humans are concerned): magic by ritual, and magic by will. Magic by ritual is something anyone can do, if they have the right books and paraphenalia. They can even do it by accident, such as Xander setting the book on fire by reading out of it.
With sufficient study, one can eventually learn magic by, which is what we see Willow and Tara doing in the latter seasons. I don’t think it’s necessarily innate: Willow had to do a lot of studying and practice just to get to the point where she could levitate a pencil. And major, hard core magic (like resurrections spells, or restoring souls) seem to still require a lot of ritual.
I think that, ultimatly, these are actually the same kind of magic. Spells require a degree of focus and willpower that most people don’t normally possess. A ritual puts the magic user into the proper frame of mind to channel the spell, but only temporarily. With practice, a human can learn to enter that state of mind with out the ritual. Even accomplished wizards still need to revert to rituals when casting extremely powerful spells, though.
Apparently, there are also ways of circumventing that process and tapping directly into major magic energies, but this is dangerous, and can carry a heavy price. This is what happens when Willow goes all dark and veiny after bad things happen to her girlfriend. My fanwank here is that part of the training and practice a wizard undergoes is learning how to control increasingly large amounts of magical energy. If they try to use a shortcut, and grab more power than they’re capable of controling, then the magic starts to control them. This happened when Willow went after Glory in season five, and that’s when she went from “regular witch” to “magic addict.” After Tara got shot, she did another huge power grab, and lost control entirely. The break between seasons six and seven, when Willow was with the coven in England, was spent helping her “digest” the huge amount of power she had unlocked in seasons five and six. What makes Willow an unusually powerful witch isn’t proximity to the Hellmouth, or genetics, or being buddies with a Slayer, but is instead due to her essential moral nature: she was able to take in so much magic energy that she turned “dark,” but still contained a strong enough core of decency to pull back. Most other mages who do what she did self-destruct, or are taken down by other powers. (Or succesfully blow up the planet, but that’s rarer.) Willow was able to make that sort of mystical power grab, and ultimatly emerge relatively unscathed, resulting in her having a huge degree of magical power at a very young age.