The difference between Psionics, Pact Magic, and Wizardry is a well known, and oft refrenced thing in the Brimstone Angels series of novels, the Elminster line, and the Drizz't line. The difference between "Arcane" and "Divine" magic is also well known and often discussed in lore. In the Elminster stories, one of the Chosen of Mystra is a bard, another was a sorcerer, and there's been talk about the difference of their magic from Elminster's wizardry. The rivalry between Wizards, sorcerers, and warlocks is another in game bit of fiction that's talked about in character. The differences between druidic and clerical magic was commented upon in one of the Sundering novels.
The difference between the major spellcasting classes is a firmly established part of the lore of the game, known and referenced by learned characters. That's seven of the thirteen known classes (even if one hasn't been formally made yet) that have a definitive in character reference. Clerics versus paladins, and rangers versus druids, are a bit more difficult, since these two classes are described, lore wise, as using the same magic as clerics and druids, pulled from the same sources. However, there are still definitive traits that make in game distinctions. Dhal, again from the Brimstone Angels series, is a fallen paladin, and several mentions of unique paladin traits have been mentioned in the novel, and thus part of lore. The same with rangers. Monks are a bit different than other classes, but their manipulation of life energy, from a lore perspective, is unique among magical effects, and has been noted upon several times in FR lore.
That's all but three classes that are specifically known about with observable difference in the default D&D setting, and all that is off the top of my head. I'd have to dig for more, but I have a more than half remembered ideas of where to look for differences between lore-bsaed, in FR known separation between barbarian training and Fighter, if not called by those names. Can't recall references between rogue and fighter, but I'm sure if I looked I could find it.
So, yes. The default lore pushes classes being a known, in character difference as part of the established setting. Sorry, but that's not really up to debate.