difference vs quarrel

difference and quarrel both are nouns.

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

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

difference (noun)	quarrel (noun)
the quality of being unlike or dissimilar	an arrow that is shot from a crossbow; has a head with four edges
a disagreement or argument about something important	an angry dispute
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

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