public holiday vs national holiday

public holiday and national holiday both are nouns.

Word	Noun	Adjective	Verb	Adverb
public holiday	Yes	No	No	No
national holiday	Yes	No	No	No

As nouns, public holiday and national holiday are synonyms defined as:

public holiday and national holiday: authorized by law and limiting work or official business

Other synonyms of public holiday include legal holiday.

public holiday (noun)	national holiday (noun)
authorized by law and limiting work or official business	authorized by law and limiting work or official business