rift vs falling out

rift and falling out both are nouns.

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

As nouns, rift and falling out are synonyms defined as:

rift and falling out: a personal or social separation (as between opposing factions)

Other synonyms of rift include breach, break, rupture, severance.

rift (noun)	falling out (noun)
a personal or social separation (as between opposing factions)	a personal or social separation (as between opposing factions)
a narrow fissure in rock
a gap between cloud masses