This is a fascinating thread - I went away and gave it some thought before coming back to it.
In terms of how I identify others - it's not about jobs, or even relationships - more about personalities (eg confident, quiet, talkative, pompous etc). I think that's maybe a reflection of the place where I live - here there are so few jobs that people just do what is available, not follow a "career" as such (if you want to do that, you have to move somewhere bigger!) - so your job is not really a reflection of "who" you are.
Myself - I think I am a mass of contradictions: talkative but quite shy, appear confident but am not at all, massive problems with self-esteem (which ease gradually as the years go by but I still stress about other people's opinions of me).
When people ask about us, I think we tend to mention the hooks we hang our different hats on - eg wife, mum, teacher etc - after all it would be a bit weird if you were asked to say a bit about yourself to a group of strangers and you said "well I lack confidence in my appearance and I've never quite got over being dumped by my first boyfriend" - we tend to give out "public" information in these situations which comes back to our different roles we play.