public holiday vs holiday

public holiday and holiday both are nouns.

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

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

public holiday (noun)	holiday (noun)
authorized by law and limiting work or official business	leisure time away from work devoted to rest or pleasure
	a day on which work is suspended by law or custom

public holiday (verb)	holiday (verb)
	spend or take a vacation