Wedding ministers are ministers of the church that choose to officiate weddings. Ministers should only be used for weddings of couples that seek to be married under their God. There are many other types of officiants for weddings for different religions or those that are nonreligious. The church of the flying spaghetti monster and church of Cthulhu both have ordained ministers capable of officiating weddings. Ramen.
Wedding officiants can be anyone that has obtained a license to perform a wedding. Officiants can be anyone from a family friend, to a judge in your local courthouse. Couples can be married in just a matter of minutes in a courthouse.