breakup vs rift

breakup and rift both are nouns.

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

As nouns, rift is a hyponym of breakup; that is, rift is a word with a more specific, narrower meaning than breakup:

Other hyponyms of breakup include breach, break, falling out, rupture, severance, break.

breakup (noun)	rift (noun)
the termination or disintegration of a relationship (between persons or nations)	a personal or social separation (as between opposing factions)
coming apart	a narrow fissure in rock
	a gap between cloud masses