All magic using beings can be termed “magician” but the term usually refers to humans. Magic is a type of energy that exists at varying levels in different areas. It is a being of it own, but you can only tell in the places with extremely high magic concentration (so high that normal non-magical folk might die or go crazy). There are many magical non-humans, with the gods being the strongest (right after magic itself).
Wizard – Places with high magic concentration have magic seep into people while in the womb. Wizards vary in power much more than magicians because of that. They need to study a lot to harness or even manifest the power. Only the most powerful wizards do not need talismans to perform magic. If strong enough, the magic seeping into them will become part of their biology, forever and irreversibly infused (at the moment; research on this continues). Then they could also be considered a sorcerer.
Cleric – Sometimes one or more of the gods give someone power and BAM ~magics~. Usually it is a very spiritual person (it can be at birth or more often that not in the late teens) so they are usually rather chill. Unless they worship a violent god or one that is affiliated with demons, etc. In that case, well, what happens happens. They don’t need a talisman to perform magic, but usually using one will enhance their power. That is unless the power granted to them from the gods comes from a blessed talisman–in that case they’re powerless without it.
Druid – Druids may start as any other type of magician, but eventually they attain another level and fuse with magic itself. Often times, this happens away from cities because the many distractions and the fluctuations in magic levels make it hard to be very spiritual, so druids are often associated with nature. This is not always the case, but that is the reason for the common depiction of druids.
Warlock – Two definitions exist, depending on who you ask
A wizard educated as an apprentice, away from the common wizard societies and formal education. Essentially, an informally educated wizard. They get a bad rap because masters who do train apprentices away from society are ones that were labeled outcasts and mavericks in the first place, and the pupils who seek a master are often outcasts and mavericks rejected from the formal magic training schools.
A magician who obtained power from a magical being (not a god) who blessed them or a talisman with it. Or they stole one. Basically they weren’t born with magic but now they have it. An wizard can become a warlock technically, if they grain some magic infusion or steal something from a demon, high elf, etc. The magic granted to warlocks is not as strong as the gods’ magic, but that also depends on how much and what type of magic the gods decide to grant.
Sorcerer – Magician who gains power from magic infused in blood. At some point in the past, their ancestors bred with magical beings or were given special blessing from the gods or a magical being or absorbed an unusually large amount of magic into their being (slightly different from the stuff that produces wizards, clerics, and warlocks). Druids could count though. The magic was strong enough to become part of their biology or something of the like, and it was transmitted to their children. Thus, sorcerers do not lose power as easily as warlocks or wizards, and are less dependent on magic concentration levels around them. Like wizards, there is considerable variation in power, depending on how far down the line you are, how closely related you are, and how powerful your ancestor was. Some needs education and talismans while other need only one or none.