The PC roles or character classes were more than just professions, they represented who a character was at his/her core.
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Somewhere down the line as classes began to proliferate and become more specialized, their meaning as a core of who the character was got replaced with becoming their job. Naturally, as classes became more narrowly defined then they became less connected to actual character identity. For most people, their profession doesn't define who they are as a person. Its the same with highly specialized classes, they don't define who the character is, only what they do.
The idea of class as profession has a long history, though. Page 18 of the AD&D PHB says that "Character class refers to the profession of the player character", and the same equation of class with profession occurs on p 7. And in the DMG, Gygax says (p 12):
When a player character selects a class, this profession is assumed to be that which the character has been following previously, virtually to the exlusion of all other activities.
Moldvay also glosses "class" as "profession": p B3.
And some specialised classes (eg druid, monk, paladin, original Aragorn-esque ranger) actually establish the identity of the character
more thoroughly then the broader classes like fighter and MU.
So I would say, rather than the conception of class narrowing from "identity" to "profession", it
changed frombeing a conception of profession and role conceived of as a whole way of life within the gameworld and hence an approach to the game, to being a mere set of mechanical abilities of little significance for how the game is actually tackled. This is part of the broader trend of disdain for the importance of mechanics that one sees beginning in the late 80s.
On p 85 of his DMG, in a discussion of the game logic of the XP rules, Gygax says:
While it is more "realistic" for clerics to study holy writings, pray, chant, practice self-discipline, etc . . . it would not make a playable game role along. Similarly, fighters should be exercising, riding, smiting pelts, tilting at the lists, and engaging in weapons practice . . .; magic-users should be deciphering old scrolls, searcing ancient tomes, experimenting alchmically, and so forth; while thieves should spend their off-hours honing their skills, "casing" various building, watching potential victims, and carefully planning their next "job". All veruy realistic but conducive to non-game boredom!
I think this, together with the discussion of "natural functions" on the following page (which include "boldly leading" for fighters, "helping" for clerics, "employing magic items" for MUs, and "acquiring extra bits of treasure when the opportunity presents itself" for thieves), reinforces the idea that class brings with it certain expectations about functions, responsibilities, etc - from which there then follows a place in the imaginary world.
Whereas by the time we get to the 2nd ed PHB or the RC (as per the passage quoted just upthread in my reply to [MENTION=6696971]Manbearcat[/MENTION]) we have the idea of personality as the separate and more important component of character role - and so we get fighters who hate violence, thieves who refuse to steal, MUs who disavow the use of magical items, etc. Playing the character comes to mean not
inhabiting the functions/capabilities of the character - which in classic D&D are determined overwhelmingly by class - but developing and then acting out some personality, to which the functions/capabilities of the character might be quite orthogonal.