fall apart vs break up

fall apart and break up both are verbs.

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

As verbs, break up is a hyponym of fall apart; that is, break up is a word with a more specific, narrower meaning than fall apart:

fall apart (verb)	break up (verb)
become separated into pieces or fragments	laugh unrestrainedly
break or fall apart into fragments	break or cause to break into pieces
go to pieces	come to an end
lose one's emotional or mental composure	separate (substances) into constituent elements or parts
	cause to go into a solution
	cause to separate
	close at the end of a session
	bring the association of to an end or cause to break up
	make a break in
	set or keep apart
	break violently or noisily; smash
	attack with or as if with a pickaxe of ice or rocky ground, for example
	release ice
	destroy the completeness of a set of related items
	take apart into its constituent pieces
	suffer a nervous breakdown
	disband
	to cause to separate and go in different directions
	discontinue an association or relation; go different ways