For questions about documents pertaining to an individual person's birth, including birth certificates, registers and indexes
Use birth-records on questions pertaining to research using birth records, such as locating or interpreting an ancestor's birth certificate.
Use parentage on questions pertaining to specifically identifying who the parents of individuals are; particularly with adoption / orphan records.
For questions about locating multiple types of records in a certain time and place, such as birth, marriage and death records, use the tag vital-records rather than tagging each record type individually.
Before government registration of births began, in many places there were simply no records of births per se. For example, civil registration began in England in 1837, and in the United States the availability of birth certificates varies greatly by state and city. Before birth records were systematically recorded by governments, to research further back one must often rely on proxy records such as baptism records. For such questions use baptism-records.