Wizards

Most people are prone to using the term "Wizard" to relate any kind of mortal or immortal to obtaining magical abilities. Although this is a common term for there 'race' there are different classes just as in the "Human" race there are different nationalities: German, African, Chinese,Puerto Rican, ect.

Mages
General magic users.

Abjurers
Defensive magic users

Cast magic on or for friends and himself

Conjurers
Cast magic for himself only

Creates armys out of creatures, or the undead

Enchanters
Cast secret magic

No one knows when the spells have been cast until enchanters have activated the spells

Invokers
Calls upon greater powers to give them the ability to cast a spell

Diviners
Branch out and attempt the powerful and dangerous magic

Necromancers
Cast dark or evil magic

Transmuter/Alterers
Cast form changing spells.

(In Harry Potter they have a class called Transfiguration)

Wild Mage
Attempt the erratic, and 'untamed' magic

Air Elementalist
Cast air type spells

Water Elementalist
Cast water type spells

Earth Elementalist
Cast earth type spells

Fire Elementalist
Cast fire type spells

Dimensionalist
Able to travel through space and time

Alchemists
Master potion makers

Shadow Elementalist
Cast shadow magic

Light Elementalist
Cast light magic

Artificer
Create magical objects