face-off vs disagreement

face-off and disagreement both are nouns.

Word	Noun	Adjective	Verb	Adverb
face-off	Yes	No	No	No
disagreement	Yes	No	No	No

As nouns, disagreement is a hypernym of face-off; that is, disagreement is a word with a broader meaning than face-off:

face-off (noun)	disagreement (noun)
(ice hockey) the method of starting play; a referee drops the puck between two opposing players	a difference between conflicting facts or claims or opinions
a hostile disagreement face-to-face	the speech act of disagreeing or arguing or disputing
	a conflict of people's opinions or actions or characters