Battle mage/magician: A type of mage that specifically knows how to fight thus the name 'battle mage', they usually end up being guards for nobles or soldiers for the country.
Alchemists: Mages/Magicians that end up using alchemy to research spells and create formula for potions and elixirs. Advanced alchemists can create artifacts.
Clerics : Mages/Magicians that are religious, they join a church after graduating and get bestowed upon divine magic (light magic) which makes them able to heal and purify things.
Dark Mage/Magician : Mages that use dark magic (forbidden) and can use curses, poison, and possibly raise the dead.