public convenience vs public lavatory

public convenience and public lavatory both are nouns.

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

As nouns, public convenience and public lavatory are synonyms defined as:

public convenience and public lavatory: a toilet that is available to the public

Other synonyms of public convenience include comfort station, convenience, public toilet, restroom, toilet facility, wash room.

public convenience (noun)	public lavatory (noun)
a toilet that is available to the public	a toilet that is available to the public