No, they're not. There is the concept in accounting and record keeping in general of the "source document". The old "Certificate of Live Birth" was the source document of birth information in Hawaii as long as it was in use. This computer generated "Certification of Live Birth" is not a source document. The source document is an original piece of paper, or the computer storage device itself where the information was originally recorded.
The originally recorded birth information is from the "Certificate of Live Birth" for all Hawaiians born when that certificate was in use. Certified copies were supplied to individuals for personal use. I don't know if it is still in use, or if birth information is now entered directly into a computer. But for Obama, that's irrelevant since he was born when the typed "Certificate of Live Birth" was in use. And, two state officials say they have examined the original, or vault copy.
The state was correct to use one term for the older typed, original source document "Certificate of Live Birth", and a different term for the non-source document, computer generated "Certification of Live Birth" printout.
Then use “source document” and non-source document. You make my point. There is no linguistic difference between certificate and certification. That you have to use circumlocutions to make your point proves my point.