commonwealth country vs state

commonwealth country and state both are nouns.

Word	Noun	Adjective	Verb	Adverb
commonwealth country	Yes	No	No	No
state	Yes	No	Yes	No

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

Other hypernyms of commonwealth country include body politic, commonwealth, country, land, nation, res publica.

commonwealth country (noun)	state (noun)
any of the countries in the British Commonwealth	the way something is with respect to its main attributes
	a politically organized body of people under a single government
	the group of people comprising the government of a sovereign state
	the territory occupied by a nation
	the territory occupied by one of the constituent administrative districts of a nation
	a state of depression or agitation
	(chemistry) the three traditional states of matter are solids (fixed shape and volume) and liquids (fixed volume and shaped by the container) and gases (filling the container)

commonwealth country (verb)	state (verb)
	express in words
	put before
	indicate through a symbol, formula, etc.