The Origin of the word Christmas
The modern word Christmas comes from the Old English Cristes mæsse, or Christ's mass. In Medieval Catholicism, this was the Mass. The word mass itself appears to come from the Latin missa, from the end of the Old Latin liturgy, where the priest dismissed the congregation, "Ite, missa est." ("Go, it is [the] dismissal" or "Ite, missa est [finita, finished].) Anyway, these words of dismissal in time became applied to the entire church service. (One wonders, were people that eager to get out?) So really Christmas is simply the liturgical celebration of Christ (really, of his birth), in a church service. For more on this, see my article "The Man Who Came in From the Cold."

The Origin of the name Santa Claus

There was a Turkish bishop of the 4th century, Nicholas, well known for deeds of charity and kindness to the poor. In accord with the Catholic custom of "promoting" various Christians to sainthood, in time he became Saint Nicholas. By way of the Dutch name of this man, Sinter Klaas, the Americans corrupted the name to Santa Claus in English.