public toilet vs privy

public toilet and privy both are nouns.

Word	Noun	Adjective	Verb	Adverb
public toilet	Yes	No	No	No
privy	Yes	Yes	No	No

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

Other hypernyms of public toilet include facility, bathroom, can, john, lav, lavatory, toilet.

public toilet (noun)	privy (noun)
a toilet that is available to the public	a small outbuilding with a bench having holes through which a user can defecate
	a room or building equipped with one or more toilets

public toilet (adjective)	privy (adjective)
	(followed by `to') informed about something secret or not generally known
	hidden from general view or use