Father Christmas means Santa Claus and he is to do with Christmas because it is a tradition and he is the one who delivers your presents and make Christmas eve a fun exiting night.
It is supposed that Father Christmas flies over the people's houses in England and puts presents under the Christmas tree and "goodies" in their fireside stockings. It was supposedly started in...
Santa Claus is Father Christmas he distributes the presents and is the one that puts the thought into Christmas. Jesus is the one that puts the religious thoughts in Christmas