Our daughter's birthparents introduce us as "Catie's parents". Plain and simple -- we are her parents. In the "world of adoption" there are a lot of qualifiers that get tossed around - using them when introducing can turn into a tongue-twister! :) If the person you are introducing the couple to is close to you, then they'll understand the relationship...No need to spell it out.

"Meet my son's parents"............ (and only if the person you're speaking to looks mystified, clarify it by saying "Adoptive parents", or if you enjoy a relaxed relationship with the couple, maybe "His other Mum and Dad")

How about asking them what they prefer?  When introducing my daughter's bmom I always ask her ahead of time what her comfort level is.

Our daughter's birthmother always introduces us as baby C's parents and we introduce her as baby C's , birthmother (and then her name), or if it is a closer relationship with whomever then, as "Mama ????." (a shortened version of her first name). Baby C's birthmother is my 2nd cousin so we have a very close family relationship and we are all very comfortable together. Her birthmom is with us on holidays and outings so we have had plenty of experience introducing her and sharing our adoption experience.

We've always been introduced as "Mallory's parents, Bert and Lisa."  She has never explained the relationship because I assume everyone she introduces us to know what Mallory's relationship is to her first mom.

Well... I have not had to do any "introducing" yet *face to face* of my daughters parents. But when I refer to them to other people, I call them by thier first name or my daughters mom or dad, sister, brother ect. Or I have gone "there" out of silliness and referred to them as "my baby mamma" and "my baby daddy". Hope that helps somewhat.

Our son's first mom usually just introduces us by our names, because people often already know our relationship.  Sometimes she'll add "my son's parents."  I wouldn't be offended if she introduced us as his adoptive parents. 

My daughter's mom introduces me as, "This is Dawn, my daughter's mother."