Hmm, in Harry Potter "wizards" seems to describe the entire human magical society, so I don't think they are using this sort of classification.
A good name for someone who only casts spells could be a magician on a conjurer.
On the other hand, when telling a story, I think it makes sense to make it so that the main character is a wizard just because it has the most cultural cachet. And most people don't want a story about debugging. So either we could be skipping over their day-job debugging (most programmers also have decent computer skills as a side-effect, so when the village is attacked by goblins it makes sense that some wizard would suddenly be flexing their more directly applicable skills). Or wizard could be something broad, like "general STEM person," and the main character is in some applied subfield. Or the magic creators could have some other job title (Mage, although that sounds a little generic for some reason... Sorcerer among people who are into games is sometimes mapped too closely to the wizard/sorcerer distinction from D&D, but not every magic system has to follow D&D tropes and it does have a good pun built in... or something like spell-weaver could be made up).
A good name for someone who only casts spells could be a magician on a conjurer.
On the other hand, when telling a story, I think it makes sense to make it so that the main character is a wizard just because it has the most cultural cachet. And most people don't want a story about debugging. So either we could be skipping over their day-job debugging (most programmers also have decent computer skills as a side-effect, so when the village is attacked by goblins it makes sense that some wizard would suddenly be flexing their more directly applicable skills). Or wizard could be something broad, like "general STEM person," and the main character is in some applied subfield. Or the magic creators could have some other job title (Mage, although that sounds a little generic for some reason... Sorcerer among people who are into games is sometimes mapped too closely to the wizard/sorcerer distinction from D&D, but not every magic system has to follow D&D tropes and it does have a good pun built in... or something like spell-weaver could be made up).