I mostly agree with Liquid, but let me add a few other comments.
Well, first I'd say, why not just think about your own life? When would YOU refer to your father or girlfriend or whomever by their job title rather than the relationship? In general, your characters should do the same.
Mostly, I'd refer to someone close to me by a title rather than relationship if the title was relevant to the context where I was speaking or writing and the relationship was not. Like if my father was a scientist and I was introducing him at a convention of a scientific society, I might well say, "Ladies and gentlemen, our next speaker is Dr Jones, professor of physics at Fwacbar University", and not, "Hey guys, my dad is up next."
But if I was introducing him to a group of friends, I would almost certainly identify him by the relationship. "I'd like you all to meet my dad." After that I might or might not mention, "he's a physics professor" or whatever.
I think that the point is not how much I want to portray myself as close to or distant from this person, but rather, what the audience cares about. The audience at a science convention probably doesn't care that the physicist who is about to speak is the father of the master of ceremonies who is making introductions. It's an irrelevant fact. Likewise if I'm introducing my new girlfriend to my parents, the most important thing to her is that they're my parents, not what their jobs are.
The more you say, the more likely you are to bring up both. If I was giving a long introduction for my imaginary physicist father, at some point I might tell some amusing story about how when I was a kid we couldn't play catch in the back yard without him talking about Newton's Laws of Motion. Or if I was telling my girlfriend about my parents, it seems likely that somewhere along the line I'd mention my father's job.
There might be times when you would deliberately keep the job title or the relationship secret. Like the girl doesn't want boyfriends to know that her father is a billionaire because she wants a man who loves her for herself and not for her money. Or the reporter doesn't mention that the person he's writing about is his sister because he doesn't want readers to think he's biased. Etc.