From: Office of Homeland Security Statistics Glossary
Child (immigration): Generally, an unmarried person under 21 years of age who is: a child born in wedlock; a stepchild, provided that the child was under 18 years of age at the time that the marriage creating the stepchild relationship occurred; a legitimated child, provided that the child was legitimated while in the legal custody of the legitimating parent; a child born out of wedlock, when a benefit is sought on the basis of its relationship with its mother, or to its father if the father has or had a bona fide relationship with the child; a child adopted while under 16 years of age who has resided since adoption in the legal custody of the adopting parents for at least 2 years; or an orphan, under 16 years of age, who has been adopted abroad by a U.S. citizen or has an immediate-relative visa petition submitted in his/her behalf and is coming to the United States for adoption by a U.S. citizen.
Accompanied minor (AM): An individual younger than 18 years old encountered by Customs and Border Protection (CBP) Office of Field Operations (OFO) who is determined to have no lawful immigration status and who is traveling with a U.S. citizen or lawfully admissible alien parent or legal guardian. Accompanied Minor (AM) data are limited to OFO encounters.
Unaccompanied alien children (UAC): Individuals younger than 18 years old encountered by Customs and Border Protection (CBP) under Title 8 authority who are determined to have no lawful immigration status and who either do not have a parent or legal guardian in the United States or do not have a parent or legal guardian in the United States who is available to provide care and physical custody.