public lavatory vs lav

public lavatory and lav both are nouns.

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

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

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

public lavatory (noun)	lav (noun)
a toilet that is available to the public	a room or building equipped with one or more toilets