breakthrough vs brainstorm

breakthrough and brainstorm both are nouns.

Word	Noun	Adjective	Verb	Adverb
breakthrough	Yes	No	No	No
brainstorm	Yes	No	Yes	No

As nouns, brainstorm is a hypernym of breakthrough; that is, brainstorm is a word with a broader meaning than breakthrough:

breakthrough: a productive insight
brainstorm: the clear (and often sudden) understanding of a complex situation

Other hypernyms of breakthrough include brainwave, insight.

breakthrough (noun)	brainstorm (noun)
a penetration of a barrier such as an enemy's defense	the clear (and often sudden) understanding of a complex situation
making an important discovery
a productive insight

breakthrough (verb)	brainstorm (verb)
	try to solve a problem by thinking intensely about it