One is Wagner's wedding March. The Wedding Chorus, which was originally the mixed chorus at the beginning of the third act of the opera Lohengreen, was named the Wedding March because it was often used as wedding music, and was later adapted into orchestra.
The former is cheerful and enthusiastic, while the latter is solemn.
According to western tradition, the bride will play Wagner's Wedding March when she enters the venue. When the couple walk out of the church, they will play Mendelssohn's wedding March.