arguing vs dispute

arguing and dispute both are nouns.

Word	Noun	Adjective	Verb	Adverb
arguing	Yes	No	No	No
dispute	Yes	No	Yes	No

As nouns, dispute is a hypernym of arguing; that is, dispute is a word with a broader meaning than arguing:

arguing: a contentious speech act; a dispute where there is strong disagreement
dispute: a disagreement or argument about something important

Other hypernyms of arguing include conflict, difference, difference of opinion.

arguing (noun)	dispute (noun)
a contentious speech act; a dispute where there is strong disagreement	coming into conflict with
	a disagreement or argument about something important

arguing (verb)	dispute (verb)
	take exception to
	have a disagreement over something