After my oldest daughter was born, I went to the local vital records office and got an exact certified photocopy of her birth certificate. Again, I do not have the actual certificate. The actual birth certificate is in the records office. I have a certified copy of the actual certificate.
A few years ago, when I couldn't find the certified copy of my birth certificate and needed one, I had my mother obtain a copy for me. I was sorely disappointed. All I got was a "certificate of live birth." It was an EXTRACT from the actual birth certificate. The extract basically said I was born on a certain date in a certain place. My parents' names are on it, but the essence of the form is that it indicates my date and place of birth are contained in a record in the office that has their raised seal stamped on the "certificate of live birth."
A "certificate of live birth" is a fairly typical way in which to issue a "copy" of a birth certificate.
The genealogist in me would rather have the copy of the actual certificate, but for most other purposes, the "certificate of live birth" is just fine.
Genealogists would consider the actual copy of the birth certificate an image copy, a derivative typically considered to be the equivalent of the original. The "certification of live birth" would technically be a transcription. Transcriptions are not necessarily bad, just different.
There is nothing unusual about a "certificate of live birth." Millions of Americans have them.
And my birth announcement appears in the local newspaper, too.