fall apart vs break down

fall apart and break down both are verbs.

Word	Noun	Adjective	Verb	Adverb
fall apart	No	No	Yes	No
break down	No	No	Yes	No

As verbs, break down is a hypernym of fall apart; that is, break down is a word with a broader meaning than fall apart:

Other hypernyms of fall apart include lose it, snap.

fall apart (verb)	break down (verb)
become separated into pieces or fragments	collapse due to fatigue, an illness, or a sudden attack
break or fall apart into fragments	stop operating or functioning
go to pieces	separate (substances) into constituent elements or parts
lose one's emotional or mental composure	make a mathematical, chemical, or grammatical analysis of; break down into components or essential features
	make ineffective
	cause to fall or collapse
	lose control of one's emotions
	fall apart