schism vs rift

schism and rift both are nouns.

Word	Noun	Adjective	Verb	Adverb
schism	Yes	No	No	No
rift	Yes	No	No	No

As nouns, rift is a hypernym of schism; that is, rift is a word with a broader meaning than schism:

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

Other hypernyms of schism include breach, break, falling out, rupture, severance.

schism (noun)	rift (noun)
division of a group into opposing factions	a personal or social separation (as between opposing factions)
the formal separation of a church into two churches or the withdrawal of one group over doctrinal differences	a narrow fissure in rock
	a gap between cloud masses