This also explains why our protagonist has time to go around doing adventures and casting spells, while many of the other wizards seem to be old greybeards living in towers. They are actually doing a totally different kind of magic, writing the spells, debugging them, etc.
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).
Magic is just programming.
https://www.goodreads.com/book/show/18616975-off-to-be-the-w...
This is more or less how AonDor magic in Sanderson's Elantris works. You spell out what you want to do in a sort of kanji language, often with unexpected results. And you have to draw the characters really accurately for it to work.
I imagine myself trying to cast a spell like that and having to go through fifty iterations to even begin to start doing the right operation without killing the person; and even when fully trained making tons of error while doing it complete with much swearing and cursing.
I then start imagining how a spell academy would create tests for spells to test of unexpected consequences on the patient etc...
It's amazing how much complexity is hidden in a simple spell in fantasy.