Xmas vs quarter day

Xmas and quarter day both are nouns.

Word	Noun	Adjective	Verb	Adverb
Xmas	Yes	No	No	No
quarter day	Yes	No	No	No

As nouns, quarter day is a hypernym of Xmas; that is, quarter day is a word with a broader meaning than Xmas:

Xmas: a Christian holiday celebrating the birth of Christ; a quarter day in England, Wales, and Ireland
quarter day: a Christian holy day; one of four specified days when certain payments are due

Xmas (noun)	quarter day (noun)
a Christian holiday celebrating the birth of Christ; a quarter day in England, Wales, and Ireland	a Christian holy day; one of four specified days when certain payments are due