state government vs regime

state government and regime both are nouns.

Word	Noun	Adjective	Verb	Adverb
state government	Yes	No	No	No
regime	Yes	No	No	No

As nouns, regime is a hypernym of state government; that is, regime is a word with a broader meaning than state government:

state government: the government of a state in the United States
regime: the organization that is the governing authority of a political unit

Other hypernyms of state government include authorities, government.

state government (noun)	regime (noun)
the government of a state in the United States	(medicine) a systematic plan for therapy (often including diet)
	the organization that is the governing authority of a political unit