public convenience vs privy

public convenience and privy both are nouns.

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

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

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

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