commonwealth vs state

commonwealth and state both are nouns.

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

As nouns, commonwealth and state are synonyms defined as:

commonwealth and state: a politically organized body of people under a single government

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

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

commonwealth: the official name of some states in the United States (Massachusetts and Pennsylvania and Virginia and Kentucky) and associated territories (Puerto Rico)
state: the territory occupied by one of the constituent administrative districts of a nation

Other hypernyms of commonwealth include province.

commonwealth (noun)	state (noun)
a politically organized body of people under a single government	the way something is with respect to its main attributes
a political system in which the supreme power lies in a body of citizens who can elect people to represent them	a politically organized body of people under a single government
a world organization of autonomous states that are united in allegiance to a central power but are not subordinate to it or to one another	the group of people comprising the government of a sovereign state
the official name of some states in the United States (Massachusetts and Pennsylvania and Virginia and Kentucky) and associated territories (Puerto Rico)	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 (verb)	state (verb)
	express in words
	put before
	indicate through a symbol, formula, etc.