I have never thought about this before since it is too hard to define and I am not interested in that role in rpg.
Here is my take:
Spell caster / magic user: the general term for people that can use magic. Unless your magic system has something else to differentiate these two apart, they are interchangeable.
Magus: spell caster, whose source of magic is the gods. Quite similar to a priest, but a priest is a servant of their god. Magus simply leeches power from the gods. Their relationship with the gods can be said to be contractors.
Magician: spell casters that figured out magic by themselves. Most of them are very talented individuals that hid among the population. Even to other spell casters, it’s not easy to spot a magician. The trickster among the magic users.
Wizard: spell casters that went through formal education in a magic institute. Wizard is a title like bachelor. Think of the like certified magic expert.
Mage: spell casters that study magic from informal education. Unlike magician, they has a mentor.
Sorcerer / Sorceress: originally conjurers. They have deep history with magic due to their ancestors being conjurers. For this reason, they don’t need to chant or call the spell to cast.
Witch: spell casters that gains power by changing themselves internally through their own concoctions. They usually lived far from the rest of civilization, cooking the best potions that makethem better. Witch coven is a community where they met after awhile to exchange information and seek assistance. Male witches are rare.
Warlock: secluded spell casters. They are famed for conducting grand rituals. Among the spell casters, a warlock is the equivalent to an artillery piece. Their magic requires heavy and long preparation, but the effect is tremendous. Warlocks are the most solitary members, since they has little to no self-defense in close combat. They have to hide within their own cave/hut which is heavily defended with their artifacts and ambush spells. Warlock are similar to witch in one aspect which is their long life. While the witches relied on their potion to buy time, warlock’s ritual borrow them extra life.
Lich: usually a wizard, mage, magician, warlock (rare) that killed themselves and retained their mind in their death body. No magus can become a lich, because the gods claim them upon death. Witches despised Liches, and considered them to be failed ones. The witches achieved long life without throwing their life away, while liches killed themselves then hide from Death. They are technically corpses that can use magic.
Shaman: usually wise members of a tribe. Their power lies in the power of the ancestral spirits of their tribe. The stronger the tribe, the stronger the shaman’s magic. Due to their nature, they are among the most knowledgeable about spirits and souls. In fact, most liches avoid conflict with a shaman.
Druid: most of them lived in a community of druid. They gains power through their connection with nature. There are rare instances when you will see a lone druid.
Necromancer: A magic user (mage, magician, wizard, witch, warlock) that study the art of animating dead materials. A lich can or can not be a necromancer.
Deathologist: the opposing school of idea to the Necromancer. A Deathologist is a believer of natural death. Act that violating the natural law of death is sacrilegious to their belief. They are experts in healing magic, dispel magic, and curse removal. They believe only death itself can grant relief. Those that willingly cause death unnecessary are sinners.