My brother has a step daughter and then they went on to have more children.
The girl was young when they met and they took their relationship very slowly and she was a tween by the time they were married and had more kids.
He always just refers to his stepdaughter by her name, as he does all his kids, but he will say she is "(wife's) daughter" if anyone were to ask for specifics. They're not generally that rude. He coached on all her teams, etc. and it rarely ever happened.
People just assume she's his daughter, and she and he are ok with this of course. They are exceptionally close.
He and his wife asked her what she would like to be called/referred to as. They felt she should decide.
She has an actual father, although not super involved. So dad/father wasn't a term she felt comfortable with. And she didn't want to be referred to as step daughter. So she's her mom's daughter. They say 'our children' in general.
My mom did the same thing (asked the girl) when asking if she could have the privilege of calling her a 'granddaughter'. The girl liked that.
*I like mamazita's way of wording it. I think calling her your daughter, honestly, is a bit disrespectful to her biological mother (we hear that a lot on here) and I know my friends who share custody with their exes would feel that way, if their ex's wives called themselves their 'mothers'.
ETA: Could you clarify if you're concerned about the word 'step' and why? I mean, I call my husband's mother "(hubby's name) mother" and not "my MIL" because it sounds somewhat more respectful when I'm introducing her ... and it puts her in context of their relationship. I think that's more applicable. That's why I think my husband always says "This is (step daughter's name)" and if needs be (Wife's) daughter (although that's rare). However, there's nothing wrong with me saying my MIL, or him saying his step-daughter. I'm sure he has, just like I say my MIL. It's not some taboo word. I think you might be overthinking it :)
And I didn't answer second part - I'm not a step mom, but a few of my friends are and my sibling. They are not parents, but also not friends. They enforce rules in their homes, (although are not the parent) but often are seen as mentors .. and may have stepped in in that role if that particular parent was absent. However, in a different capacity. They leave parenting strictly to parent - and same with consequences to behavior, etc. However, their home, their rules .. to a point, and they are not buddies. No.