At some point during our last game session, I turned to our warlock and said "I expected you to help us with that, sorcerer", and his answer was "I'm not a sorcerer, I'm a warlock". My reply was "warlock, sorcerer, wizard, conjurer, or mage, I don't care, it's all the same", to which he answered, "it's the same for you, who have no understanding of arcane matters".
So, is character class an in-world concept in your campaigns? Could the mightiest sorcerer in your world be in fact a 20th-level wizard? If my oath of vengeance paladin was trained as part of a monastic order, would other people disagree if he referred to himself and other members of his order as warrior monks and tell him that monks are supposed to fight unarmored?
To answer my own question, except for some very specific situations, like druids in AD&D 2e, I never treated character class as an in-world concept. In my own games, a light-armored fighter with a criminal background does not see himself as fundamentally different from someone with levels in the rogue class.
What about your own campaigns?
My answer is this: "Definitely. Sorta. No. Did you know vlad tepes officially held the rank of paladin? Also knight. Also prince. Also count. He did btw." Also a healthy dose "its complicated" is in my answer.
Consider the following: a cleric could likely be in game known as or think of itself as or be called a cleric, priest, saint, bishop, monk, or cultist and cleric is not even the most likely word for him to be known by.
Or by their other profession. Maybe a preacher, doctor, teacher, archivist or whatever. Maybe multiple.
A favored soul: cleric, priest, saint, favored soul, the chosen one (watch out for sand and evil space wizards), bishop, cultist, warlock, sorceror, demigod, godling, half-mortal, cambion, miracle man, and so on.
Or by their other profession. Maybe a poet, seer, theif, cult leader or whatever. Maybe multiple.
Paladin: paladin, cleric, saint, knight, bishop, and so on.
Or by their other profession. Maybe a veteran, war hero, soldier, protector, body guard, guard, priest or whatever. Maybe multiple.
This list goes on and on for basically most classes i can think of. Its one of those things where its kinda ingame. But it is kinda not too. And it really is character, region, and language specific. And you even have this inter classially (that is not a word. I know). In many cases a wizard is a guy who was born already a powerful sorceror and gained wizard schooling simply because his family couldnt possibly see him not going to the mage school as not being a waste of his raw talent and as a result out if game they progress as a wizard but in game they already have the innherent arcane potency and natural talent of a sorceror which is why they were schooled as a wizard in the first place but they are known by their friends to legitimately be both (as they literally have sprcerous talent but they focused it into thebdiscipline of a wizard.).
Look at vecna for example. Probably is a favored soul in the truest sense of the word. Is a god. Is a wizard. Has knowledge more fundemental than true naming. Is "sorcerous". And so on. Many things apply. Even if out of game on paper hes buolt strictly as a wizard with an undead template and divine ranks. In game hes so much more.