advert vs publicity

advert and publicity both are nouns.

Word	Noun	Adjective	Verb	Adverb
advert	Yes	No	Yes	No
publicity	Yes	No	No	No

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

advert: a public promotion of some product or service
publicity: a message issued in behalf of some product or cause or idea or person or institution

Other hypernyms of advert include packaging, promo, promotion, promotional material.

advert (noun)	publicity (noun)
a public promotion of some product or service	the quality of being open to public view
	a message issued in behalf of some product or cause or idea or person or institution

advert (verb)	publicity (verb)
make a more or less disguised reference to
make reference to
give heed (to)