The world of Witcher is not a D&D, in most cases, the different names are just indeed names - the same person might be called "witch" by an angry crowd or "enchantress" by her potential clients. So there is no real difference between wizards, mages, enchanters, witches - other than the name. They all undergo education (in one way or another) that helps them to control the primal chaos and taking the power from the elements. There is not much information about Druids, but it seems that their magic works in a similar fashion, however, they are obviously more "eco-friendly"<sup>1</sup> and refuse to take power in such quantities as wizards.

>“You focus yourself quickly. Let me remind you: control the flow of the force. You can only emit as much as you draw. If you release even a tiny bit more, you do so at the cost of your constitution. An effort like that could render you unconscious and, in extreme circumstances, could even kill you. If, on the other hand, you release everything you draw, you forfeit all possibility of repeating it, and you will have to draw it again and, as you know, it’s not easy to do and it is painful.”


Witchers know only very basic magic which they call "signs" - they can push things, create a small fire or a force field etc - it is all they might need in a fight with a monster. Their magical power comes from special elixirs which they take before the fight.

>“The so-called Sign of Aard, Ciri, is a very simple spell belonging to the family of psychokinetic magic which is based on thrusting energy in the required direction. The force of the thrust depends on how the will of the person throwing it is focused and on the expelled force. It can be considerable. The witchers adapted the spell, making use of the fact that it does not require knowledge of a magical formula—concentration and the gesture are enough. That’s why they called it a Sign.

When Geralt tried to use the Sign without elixirs, he was surprised that it worked:

>Geralt put his fingers together and struck the burning pile with the Aard Sign. He did not expect any great effect, since he had been forced to make do without his witcher elixirs for several weeks. But he succeeded nonetheless. The pile of branches exploded and fell apart, showering sparks around.


It is rare, but priests also can sometimes use magic, but its source of it is a bit confusing to wizards - but it seems that it is somehow different and indeed connected to some real gods (like Lady of the Lake or Melitele).

Finally, there are psions, oracles and other one-trick-ponies that have some sort of inherited magical power:

>‘I’ve got pure aitch-es-pee, which means first category psi, without the gift of pee-kay. To be precise: I can hear other people’s thoughts and speak remotely with a sorcerer, elf or other psionic. And I can give orders using thought. I mean: make someone do what I want them to. I can also do pre-cog, but only when I’m under.’ <br />
‘Please enter in the proceedings that the witness, Joanna Selborne, is a psionic, with the gift of hypersensory perception. She is a telepath and tele-empath, able to carry out precognition under hypnosis, but without the ability of psychokinesis. The witness is admonished that the use of magic and extrasensory powers in this chamber is strictly prohibited. 


<sup>1 - While the only druid we know from the name is Mousesack, there are others mentioned: one group of druids demands from a king to regulate the fishing industry (and it is refused, because "the ocean is so big so humans can never harm it"), second group with the help of driads puts a more effective ban on de-barking oaks, which causes a small revolution in the tanning industry, smartly used by a certain doppelganger. But are druids really eco-hippies? We don't really know. </sup>