Father Christmas vs Santa Claus

Father Christmas and Santa Claus both are nouns.

Word	Noun	Adjective	Verb	Adverb
Father Christmas	Yes	No	No	No
Santa Claus	Yes	No	No	No

As nouns, Father Christmas and Santa Claus are synonyms defined as:

Father Christmas and Santa Claus: the legendary patron saint of children; an imaginary being who is thought to bring presents to children at Christmas

Other synonyms of Father Christmas include Kriss Kringle, Saint Nicholas, Saint Nick, Santa, St. Nick.

Father Christmas (noun)	Santa Claus (noun)
the legendary patron saint of children; an imaginary being who is thought to bring presents to children at Christmas	the legendary patron saint of children; an imaginary being who is thought to bring presents to children at Christmas