In Singapore the terms "certificate of registration of birth" and "birth certificate" seem to be used interchangeably to refer to the same document:
"3 The Certificate of Registration of Birth is prepared in 2 copies. One copy is retained by the Registrar while the other copy is laminated and issued to the informant. The fee for a birth certificate is S$18.00. For births registered at the respective maternity hospitals, these centres may charge an additional administrative fee on top of the fee for a birth certificate"
https://www.ica.gov.sg/docs/default-source/ica/stats/annual-..."8. For a certificate of registration of birth $18."
https://sso.agc.gov.sg/SL/RBDA1937-R1?DocDate=20141001&ViewT...If the copy originally issued to the informant is lost a certified copy can be obtained for S$40. They call this a birth extract.