Русско-англо-русский юридический словарь

Adoption differs from fostering in a number of ways. Adoption is a legal process by which all parental rights and responsibilities are permanently transferred to the adoptive parents by a court. The child legally becomes part of the adoptive family, as if they had been born into it, and subsequently (usually) take the family’s surname. (PracticingParents.com)

An adoptive parent is a person who becomes the parent of a child through adoption. (Legal Information Institute)

Thousands of children are successfully adopted each year, but a small number of cases will end in failure. So what makes an adoptive parent return their child into care? (BBC News)

foster care: temporary care provided to children in settings outside their family of origin and by individuals other than their natural or adoptive parents. [...] Typically, a child is placed with a family approved for foster care and paid a fee for such by a public child welfare agency. (APA Dictionary of Psychology)