public relations vs publicity

public relations and publicity both are nouns.

Word	Noun	Adjective	Verb	Adverb
public relations	Yes	No	No	No
publicity	Yes	No	No	No

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

public relations: a promotion intended to create goodwill for a person or institution
publicity: a message issued in behalf of some product or cause or idea or person or institution

Other hypernyms of public relations include packaging, promo, promotion, promotional material.

public relations (noun)	publicity (noun)
a promotion intended to create goodwill for a person or institution	the quality of being open to public view
	a message issued in behalf of some product or cause or idea or person or institution