quarrel vs bicker

quarrel and bicker both are nouns.

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

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

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

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

quarrel (verb)	bicker (verb)
have a disagreement over something	argue over petty things