Different just means different. It doesn't mean bad.
The fact of the matter is that being adopted does make you different in your family. If breast cancer runs in the females in the family, the adopted daughter does not have increased chances of developing breast cancer like a biological daughter does. You can't say that an adopted child is just like a biological child because it just isn't so. This DOES NOT mean that an adopted child is inferior or less loved than a biological child. Emotionally, they are just as much part of the family as any of the blood relations. Physically, though, it just isn't so.
If an adopted child give family medical information to their doctor for their adopted family, that could lead to confusion and mis-diagnosis and be a dangerous situation. The adopted child has to know the difference for their own well being.
Of course adopted children are different biologically - I don't think anyone would dispute that. But often when people say different, they do mean inferior. Its very subtle, but its there.