You can only get a certified birth certificate from your state's Department of Human Services. It is often watermarked to prove its legitimacy.
A certificate of live birth may have been given to your parents before leaving the hospital after you were born. However, this has not been certified by your state's Department of Human Services.
To get a U.S. passport, you must have primary evidence of U.S. citizenship. A certified birth certificate should satisfy this requirement, but a certificate of live birth will not.
Other documents that should fulfill the requirement are a previous U.S. passport, a consular report of birth abroad, a naturalization certificate or a certificate of citizenship.
You must bring the appropriate document, in person, along with a photo ID, if this is your first time getting a U.S. passport. The photo ID can be a driver's license, military or government ID, or a naturalization certificate.