quarrel vs bust-up

quarrel and bust-up both are nouns.

Word	Noun	Adjective	Verb	Adverb
quarrel	Yes	No	Yes	No
bust-up	Yes	No	No	No

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

Other hyponyms of quarrel include affray, altercation, fracas, bicker, bickering, fuss, pettifoggery, spat, squabble, tiff.

quarrel (noun)	bust-up (noun)
an arrow that is shot from a crossbow; has a head with four edges	a serious quarrel (especially one that ends a friendship)
an angry dispute

quarrel (verb)	bust-up (verb)
have a disagreement over something