A birth child is a child that is biologically related to a mother and father. Usually this term is used in the adoption circles to identify and differentiate between the relationship of an adoptee to his or her adoptive parents and birth parents. It's not necessarily the most appropriate term for an adoptive parent to use for biological children, as this can make the adoptee feel more singled out and less attached to his or her adoptive family. However, it's fairly common for birth parents to use.
Being the parent of a birth child placed in an adoptive family does not mean the parent has parental rights. Once parental rights are either voluntarily or involuntarily terminated, the birth parents solely have their biological relationship with a child and no legal responsibilities observed.
In some states, birth mothers who have arranged for an infant placement must wait three to five days before giving their consent to the adoption being finalized. During those days, the birth mother may decide to keep and raise the birth child. The birth father, if involved with the adoption process, may decide to surrender his parental rights to his birth child any time before the birth and has a small window to revoke his consent after the birth.
The transition from a birth child to an adoptive child by any other name would still be what it is, the adoption of parental rights and legal promise to raise the child as if he or she was the adoptive parents' birth child.