dispute vs argue

dispute is a noun but argue is not a noun.

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

As verbs, argue is a hypernym of dispute; that is, argue is a word with a broader meaning than dispute:

Other hypernyms of dispute include contend, debate, fence.

dispute (noun)	argue (noun)
coming into conflict with
a disagreement or argument about something important

dispute (verb)	argue (verb)
take exception to	have an argument about something
have a disagreement over something	give evidence of
	present reasons and arguments