And yet we can argue the reverse as well: so many distinct things are "wizards" or "fighters" or "barbarians" (that last one often by some other name) in fiction that it would be impossible to force a single archetype on any of them.
Harry Potter characters are called "wizards" (or "witches"), yet the closest gameplay equivalent would need an innate ability to use magic and spells which can be used repeatedly, which are mechanics associated with sorcerers and warlocks. They do need training and practice to perform magic, sure, but they do not "get their power from knowledge," in HP you are either born with magic power or you aren't, there's no middle ground. "Fighter" is often used for characters who have legit actual magic powers (Aragorn), while "hunters" or "rangers" cover an enormous spectrum from completely ordinary trackers with no magic whatsoever to borderline druids.
It's not just "two different types," it's whole spectrums or even polydimensional spaces of characters, all of which fit under a single umbrella and many of which work by radically different rules within their local context. Gandalf is a completely different kind of being from Harry Potter or Dr. Strange, who are mutually radically different from one another, and not even one of them works the way D&D Wizards work.