Mage

A mage is a wizard/witch/sorcerer. A human capable of casting magical spells.

Magic
Magic is another word for the energies that make up the world. All of these energies come from the shadow world, and bleeds into the material world, forming everything. Consult mage: the awakening for more information on magic.

Black Magic
The essense of negativity, also the only magical energy that bleeds into the physical world, but doesn't form anything at all. Black magic is quite powerful because it also bleeds into the twilight zone and further on into the realm of the dead, as affects more zones than any other type of magic. Death magic from Mage: the awakening is essentially black magic.

Magical users
Many people can use magic, ritualists, vampires, werewolves, mages and so on.

Only mages have the potential to gain full control over it, while certain aspects of magic comes much easier to other kinds of supernatural creatures. Certain vampires have managed to learn full control over magic even beyond death, however, so there seems to be some yet to be understood rules of magic that will perhaps be defined in the future.

Mages in particular have no specific way of being organized or categorized (no watchtowers), but they organize locally, and have a few global organizations (Guardians of the Veil, as well as the Silver Ladder and the Mysterium, but membership is not mutually exclusive, and only a select few high standing mages are members).