augury vs omen

augury and omen both are nouns.

Word	Noun	Adjective	Verb	Adverb
augury	Yes	No	No	No
omen	Yes	No	Yes	No

As nouns, omen is a hyponym of augury; that is, omen is a word with a more specific, narrower meaning than augury:

Other hyponyms of augury include war cloud, portent, presage, prodigy, prognostic, prognostication.

augury (noun)	omen (noun)
an event that is experienced as indicating important things to come	a sign of something about to happen

augury (verb)	omen (verb)
	indicate, as with a sign or an omen