public convenience vs bathroom

public convenience and bathroom both are nouns.

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

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

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

public convenience (noun)	bathroom (noun)
a toilet that is available to the public	a room (as in a residence) containing a bathtub or shower and usually a washbasin and toilet
	a room or building equipped with one or more toilets