Donald Trump and various other "birthers" (as well as non-"birthers" like Pat Robertson) express concern that Pres. Obama has released copies of his "Certificate of Live Birth" and not his actual "birth certificate". Mr. Trump has also stated that the Presiden't bith certificate is a "sealed" document, as was his own but the President only needs to give permission to unseal it. As an epidemiologist, I have often worked with birth and death certificates and the only birth certificate I have ever heard of being sealed are those of adopted children, but the law may be different in New York where Trump claims he was born -- have you seen his birth certificate. In any case, Obama's birth record clearly is not sealed since copies have been issued.
As to the difference between "certificate of live birth" and "birth certificate", that is simple to answer. There is none. The formal name for a birth certificate is "certificate of live birth". That is what yours is called; what mine is called; what Donald Trump's is called; what Barack Obama's is called. A lot of people have a fancy certificate issued by the hospital where they were born that they think is their birth certificate. But if they try using it as proof of age or citizenship, they will find it is a legally meaningless scrap of paper.
The simple truth is that the President released a certified copy of his birth certificate prior to the last election. Officials at the state department of health in Hawaii have confirmed that it is genuine and accurate. Anyone who wants to continue believing that Pres. Obama was born in Kenya (or Indonesia or on the Moon) has every right to do so. But their belief is as factually false as that of those who believe the world is flat, that humans and dinosaurs roamed the Earth at the same time, that fluoridated water causes cancer, or that the Apollo moon landings were faked.