Public Marriage License - In California, a Public Marriage License is required to be legally married and allows for your ceremony to take place anywhere in the State of California, requires at least one witness who is present at the ceremony and the record of marriage is made publicly available.
A confidential marriage license differs in the following elements: Parties to the marriage must be living together already, there are NO witnesses required, your wedding officiant is NOT considered a witness; and the record of marriage is ONLY available to the named parties on the marriage license. Celebrities typically obtain confidential marriage licenses, but anyone may request one.
Marriage Licenses can be obtained at any California County Clerk's Office.
NOTE: I reference California requirements because this is the state in which I reside and am most familiar with the regulations.