quarrel vs difference

quarrel and difference both are nouns.

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

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

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

quarrel (noun)	difference (noun)
an arrow that is shot from a crossbow; has a head with four edges	the quality of being unlike or dissimilar
an angry dispute	a disagreement or argument about something important
	a variation that deviates from the standard or norm
	the number that remains after subtraction; the number that when added to the subtrahend gives the minuend
	a significant change

quarrel (verb)	difference (verb)
have a disagreement over something