Traci,
Errrrr is right!!
Just thinking out loud here and with the benefit of time to think about it (as opposed to coming up with something on the spot)...I would probably say something like, "That's great that she was able to find her birthparents (or biological parents)...I think that is a connection that many adoptees long for that people who were not adopted don't always understand. (And if at this point she didn't correct herself on her choice of the word "real" as opposed to "birthparent" because sometimes people catch that on their own, I would add....) "But as a mom who adopted her children, I consider myself Joshua and Lydia's "real" mom. I know you didn't mean to imply otherwise, but sometimes our choice of words can be taken the wrong way."
At which point she would probably apologize and say that wasn't what she meant...and you could say, "I know you didn't, and people use it all the time, but to someone whose life has been blessed by adoption, it carries a different meaning."
To me, the idea is not to make her feel bad, but to give her the benefit of the doubt AND to help her think about her choice of words. I think people who are not familiar with adoption don't give it much thought and sometimes the "language" is foreign to them.