A birth certificate is a vital record that documents the birth of a child. The term "birth certificate" can refer to either the original document certifying the circumstances of the birth or to a certified copy of or representation of the ensuing registration of that birth. Depending on the jurisdiction, a record of birth might or might not contain verification of the event by such as a midwife or doctor.
However, the certification of live birth leaves out all of the details and is merely verification that one was born in a particular state so that one may qualify for a social security number or to attend school. In other words, it serves the same purpose as a certificate of live birth in that it verifies that one qualifies for various pivileges granted those who are natural United States citizens.