holy day vs holiday

holy day and holiday both are nouns.

Word	Noun	Adjective	Verb	Adverb
holy day	Yes	No	No	No
holiday	Yes	No	Yes	No

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

holy day (noun)	holiday (noun)
a day specified for religious observance	leisure time away from work devoted to rest or pleasure
	a day on which work is suspended by law or custom

holy day (verb)	holiday (verb)
	spend or take a vacation