is a birth certificate the same as a certificate of naturalization
You may use a certificate of citizenship or a naturalization certificate, to prove that you are a US citizen. But both the documents are not the same. A US citizenship certificate is granted to a person who acquires or derives citizenship from his US citizen parents.
No. A birth certificate is issued after you are born, usually in the city and state where the birth took place. Barack Obama's birth was recorded in Honolulu, Hawaii, for example.