This is a random thought that came in my mind while waiting for the tram.
So in Hungary we have this thing that Jesus himself brings the Christmas gifts. We call him Jézuska, which means something like little Jesus, like you'd say Jesusito in Spanish.
We still have Saint Nicholas, Santa Claus but he comes on 6th December (Nicholas day) and usually brings smaller gifts like chocolate, fruits, and if you were bad, a twig that is to whoop your ass.
But on 25th Jesus himself comes and brings the big gifts.
Do you have something else than St. Nicholas in your country?
Whenever I try to explain this Jesus thing to foreigners, they are confused.
Edit:
Interestingly you won't see depictions of Jesus carrying gifts. The mascot of Christmas is still Santa everywhere.