Magic... what is magic? Mr. Webster defines it as 1 the use of charms, spells, etc in seeking or pretending to control events 2 any mysterious power 3 the art of producing illusions by sleight of hand. So where does Mr. Webster's definition come into play with those who practice magic? It falls between 1 and 2.
There are as many varieties of magic as there are stars in the sky. While there are central cultural "brands" of magic there is no doubt thousands of variations of these central brands.
European and American magic is largely based in the powers of Earth & its mystic ties to other realms. Chinese magic is largely based in ancestral bonds, traditions and mystic ties between man and the unseen. Tribal magic is based largely in religion, mono or poly-theistic entities who govern and guide magic in conjunction with mystic bonds. And the common thread between them all is the mystic association of man with entities and gods/goddesses who exist outside of our world.
These links provide a brief synopsis of some of the recognized and rarely recognized types of magic and tools involved in magic.