The words for magic users can be generic or imply meanings. The phrase “magic user” is a catchall that includes everything: wizards, mages, sorcerers, magicians, necromancers, witches/warlocks, and more. Many of these are virtual synonyms that carry no specific meaning unless we decide to differentiate them.
“Magician” sometimes implies a trickster or a charlatan. If we have true magic users and charlatans, “magician” might be for the latter and seen as an insult. On Earth, a magician is an “illusionist,” who appears to be doing magic. Such people can exist on a world with actual magic, so it’s likely there’s a word for them, and real wizards hate being considered one. This adds a dynamic. If we use “magician” for real magic users, we need another term, such as “trickster,” or “illusionist,” for these other guys.
“Mage” is familiar to fantasy audiences as a synonym for magician, but some haven’t heard this term. A simple reference will educate them, like this example: “Kier was a mage, or magician, of great renown.” This is slightly better than, “Kier was a mage, or wizard,” because the first ties “mage” and “magician” together better than “mage” and “wizard.” The word itself is archaic and fell out of usage until fantasy games like as Dungeons & Dragons revived it.
If we’ve invented types of magic for our setting, each needs a name. The inhabitants will have named them even if we try to skirt this issue. We can append other words to it, such as “high magic” and “low magic,” or create new words altogether, like my “valendry” from Llurien. We can also use the words in this section to refer to different practitioners.