quarrel vs dispute

quarrel and dispute both are nouns.

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

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

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

As verbs, quarrel and dispute are synonyms defined as:

Other synonyms of quarrel include altercate, argufy, scrap.

quarrel (noun)	dispute (noun)
an arrow that is shot from a crossbow; has a head with four edges	coming into conflict with
an angry dispute	a disagreement or argument about something important

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