I'm not a fan with either Mom being called "real Mom." I would never presume to call myself that and I would never call Cupcake's Mom that either. To me, she's not her REAL Mom, she's her Mom. Real to me sounds a little slap in the face-ish to whoever isn't the "real" Mom. The way I see it we're both real.
I personally don't like birthmom because it was a label that was put on me in the hospital and by the social worker and always was used with a negative and "less than" tone. That's my own personal experience though and because of that, I prefer first mom.
Why? Because I was Cupcake's Mom first. Doesn't mean that I come first or that I rank first or anything like that. Just chronologically first.
So I use first mom for me, and Mom for Cupcake's Mom. No "real," no "adoptive," no "second." The only time I use a qualifier is if it's a confusing explanation with lots of characters and I'll say "her aMom." But other than that, I just say Cupcake's Mom
