As for " the absurd number of specialized pure spell users that were really hard to tell apart except for their base spell lists.", that's true. To most outsiders there is no difference between a Seer, Mentalist, Illusionist, Magician, Sorcerer, or Mystic. To the average person, they would all fall under the category of "Mage". (The spell user in question might find this insulting, but it is still true.)
But the point of the spell user in question finding this insulting is the point of having distinctive naming for the distinctive professions. RL case in point: To most outsiders there is no difference between the "guy working in computers" and the "other guy working in computers", yet anyone "working in computers" knows that a network admin. isn't the same than a security specialist who isn't the same than a software developer who isn't the same than a tech. support. Does that mean, though, that's it's completely useless to make a distinction between the latter ones? I don't think so.
More down-to-earth, all swords are, well, swords. Doesn't that mean it's totally useless and serves no purpose to make a distinction between them?
Sure, most spell users only differ by their base spell lists, but that's the very point of giving them different naming. Classification, categorization, the very reason why such matters are done, because they make understanding of an unknown factor easier. On the meta level, that makes communication between players (and GMs) easier: if one speaks about his "Forcemage", every knows roughly what's he able to do, and in which fields he specializes, removing the need for "So, I play a mage"/"Oh? And what can you do,
exactly" because a "mage" would be such a vague term, it wouldn't help much understand what a character does. On a meta-level, it also helps a GM defining his NPCs: instead of writing "mage" for all his mages, of writing "mages specialized in (paragraph detailing said specializations)...", he could just write "Magician", "Forcemage", "Runemaster" and immediately understand the kind of characters they are.
On a meta level applied to actual gaming, this same help is given for spells giving information about "profession"; while it's true that such spells probably merely give an understanding of what a character can do ("According to the spell, the guy is a mage, and knows about Essence magic dealing with the fire, ice, air, earth, water and light"), it helps understanding to rather give distinctive names.
On a gaming level, mages are among the most educated professions, and in most worlds are formed in magic schools, universities and the like. As such, I do personally think they're organized by abilities/school options/classes and make the distinction, the same way WE do make a difference in naming between a first year in literature studies, a first year in computer sciences, and a second year in business administration. So, the same way, magical students would make a difference in naming between a Magus, a Magician, a Shadow Mage and an Alchemist.