I just always feel like people assume that kids live with mom and "step-mother" just means "Daddy's wife." But I've raised my kids from toddlers to teens; they live with us, and I'm their primary caregiver. Their mom is not around as much as I'm sure she would like to be.
We don't really use the step and half labels, either. My six-year-old daughter is the only one who seems to really have an issue with it, which I think stems from jealousy. The oldest two have another brother and two sisters on their mom's side, and one of the girls is about six, and my daughter *really* wants to be close to her. Unfortunately it's not really feasible since we live so far apart, so she gets upset and says things like, "A is not my *real* sister. She's just my step-sister." I usually say, "No, she's your half-sister, but that doesn't matter. What matters is that she loves you, and that makes her your real sister."
I hope my kids grow up seeing that blood relation is not that important. More than half my family is not "blood related" to me. My dad is adopted, I have a step-dad and two step-brothers (not to mention step-grandparents), plus my step-brother has a step-daughter, and not to mention my husband's whole family (who are all awesome)! Love is what matters.