Babies snatched from ambivalent birth mothers. Crying toddlers ripped from their families by birth parents who changed their minds. Those are the media images. They have little to do with the reality experienced by most adoptive families. As Miss Manners points out, they are not polyester.
Language makes a difference.
We should call them that family's children. We are the people who were sleep-deprived during their infancy. We are the people who paid for their braces. We are the people who cry with them when things don't go well. We are the people who live through their teenage years.