In the U.S. many births were not documented if the child was born at home, or somewhere other than a hospital, especially if the birth Mother lived in a rural area. Even if the child was born at a doctors office, it may not have been recorded until many years later when the child is grown and would need a record of birth. These are called "delayed births" and generally a family member, neighbor, or anyone who was at the birth or who had knowledge of the birth would be the informant on the certificate.
As for miscarriages, if the miscarriage occurred early in the pregnancy, most likely there would not be a record. If the miscarriage occurred later in the pregnancy where the child may have survived, it would be a stillbirth, There might be a birth and death record, but it would depend on the time period.