come apart vs fall apart

come apart and fall apart both are verbs.

Word	Noun	Adjective	Verb	Adverb
come apart	No	No	Yes	No
fall apart	No	No	Yes	No

As verbs, come apart and fall apart are synonyms defined as:

Other synonyms of come apart include break, separate, split up.

come apart (verb)	fall apart (verb)
become separated into pieces or fragments	become separated into pieces or fragments
	break or fall apart into fragments
	go to pieces
	lose one's emotional or mental composure