argue vs quarrel

argue is not a noun while quarrel is a noun.

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

As verbs, quarrel is a hyponym of argue; that is, quarrel is a word with a more specific, narrower meaning than argue:

argue (noun)	quarrel (noun)
	an arrow that is shot from a crossbow; has a head with four edges
	an angry dispute

argue (verb)	quarrel (verb)
have an argument about something	have a disagreement over something
give evidence of
present reasons and arguments