There may easily be more than one copy of your relative’s birth record. There could be the original birth certificate. There may be a register or summary record that includes a transcription of what was on the original certificate. There could be local and state copies of the birth certificate.
Because birth registration is governed by state statute and has changed over time, what is true in one state at one point in time is not necessarily true elsewhere or at a different time. New England states usually keep these records at the town level.
Local registration of records generally begins before state registration.
Determine what registration was taking place where your ancestor lived at the time of their birth. “Where to Write for Vital Records” has links to information on records agencies for specific states. Also check the FamilySearch catalog for the state and local area of interest.