breakup vs annulment

breakup and annulment both are nouns.

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

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

breakup: the termination or disintegration of a relationship (between persons or nations)
annulment: (law) a formal termination (of a relationship or a judicial proceeding etc)

Other hyponyms of breakup include splitsville, invalidation.

breakup (noun)	annulment (noun)
the termination or disintegration of a relationship (between persons or nations)	(law) a formal termination (of a relationship or a judicial proceeding etc)
coming apart	the act of abrogating; an official or legal cancellation
	the state of being cancelled or annulled