I think a single mom would be defined as someone not with the biological father. I have dated quite a few guys but never have they stepped up to play a fatherly role because I dont ask them too. I have had a hard time even letting them get onto my kid. It's just part of my nature. If you are pretty serious with someone and live together, they might take it upon themselves to help you with him and take on that role.
Unless the guy is just absolutely amazing right off the bat or has known you and your kids from birth, then he might take on a huge responsibility. Me and my ex have a mutual friend that has been around our kid since the day he was born. Whats bad, is that at times my sons dad wasnt around, our friend would be more of a father to my son then the biological dad.
Wanna hear something funny?!? My ex has even been asked a couple of times what it feels like to be raising his best friends son. And there has never been anything between me and the friend.. he has just always been there before birth and after... ((((( just thought i would throw that out there)))))
I agree that it is a mom who is not with the biological father. I was with my daughter's dad but we weren't married and I wouldn't have considered myself a single mom then.
It's kind of funny as I consider myself a single mom since I'm not with her dad but he does see her, doesn't pay any child support but I do get a break and I called a friend a single, single mom since her ex doesn't see their child at all so she rarely gets a break.