Tried to post on the FC vs SC thread but couldn't so have added here what I tried to write!
Had to google the origin of each (sad I know!)
It would seem that Santa Claus is bastardised pronunciation of Sinter Klaas (Dutch name for Saint Nicholas) but is actually the combination of the two religious personas of Saint Nicholas and Christkindlein, both taken to America from Europe as it was settled. Apparently Saint Nicholas (being venerated by Catholics as a saint) was dismissed by Protestants during the Reformation who began to attribute gifts given to a representation of the infant Jesus (the Christ child, or "Christkindlein").
Father Christmas is a separate character entirely, and he comes from an old English pagan midwinter festival and dressed in green to symbolise the returning spring. He was known as ?Father Winter' or ?Old Man Winter'. He didn?t give out presents, but he joined in with general feasting. He is shown in A Christmas Carol as the ghost of Christmas present.
But they all seem to be muddled into the same character now anyway, where names are interchangeable!