falling out vs schism

falling out and schism both are nouns.

Word	Noun	Adjective	Verb	Adverb
falling out	Yes	No	No	No
schism	Yes	No	No	No

As nouns, schism is a hyponym of falling out; that is, schism is a word with a more specific, narrower meaning than falling out:

falling out: a personal or social separation (as between opposing factions)
schism: the formal separation of a church into two churches or the withdrawal of one group over doctrinal differences

falling out (noun)	schism (noun)
a personal or social separation (as between opposing factions)	division of a group into opposing factions
	the formal separation of a church into two churches or the withdrawal of one group over doctrinal differences