Adopted children have two families; birth and adoptive. One brings them into the world, one raises them. That said, yes, a child
does have two Mothers. (And two Fathers.)
One raises the child, does all of the necessary "yuck" work that comes with Motherhood and usually gets to use the endearing term of "Mommy." One brings the child into the world and entrusts that the Other Mother will be able to do the "yuck" work in the best possible fashion. The birthmother makes a parenting decision on who will raise her child.
Yes, an adopted child has two Mothers.
However, there are boundaries for each family. One doesn't necessarily have to REFER to the Other Mother as a "Mom." I do not expect the Munchkin to call me Mom, though I would never tell her, "Do not EVER call me that!" If her Mom is fine with it, I am fine with it. She does/will know that I am her birthmom, or, as I'm taking a liking to, FirstMom. If D (amom) was uncomfortable with the thought of me ever being referred to as Mom or Mother, it would be a different story but she, herself, asked me why I didn't just say I was simply Munchkin's Mother. Every family is different.
But, the fact remains, no matter what you call it, an adopted child has two families. It doesn't make the Mom who kisses the boo-boos any less of a Mom.
