Christmas Day vs public holiday

Christmas Day and public holiday both are nouns.

Word	Noun	Adjective	Verb	Adverb
Christmas Day	Yes	No	No	No
public holiday	Yes	No	No	No

As nouns, public holiday is a hypernym of Christmas Day; that is, public holiday is a word with a broader meaning than Christmas Day:

Christmas Day: a Christian holiday celebrating the birth of Christ; a quarter day in England, Wales, and Ireland
public holiday: authorized by law and limiting work or official business

Other hypernyms of Christmas Day include quarter day, feast day, fete day, holy day of obligation, legal holiday, national holiday.

Christmas Day (noun)	public holiday (noun)
a Christian holiday celebrating the birth of Christ; a quarter day in England, Wales, and Ireland	authorized by law and limiting work or official business