public toilet vs bathroom

public toilet and bathroom both are nouns.

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

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

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

public toilet (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