state vs commonwealth

state and commonwealth both are nouns.

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

As nouns, state and commonwealth are synonyms defined as:

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

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

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

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

state (noun)	commonwealth (noun)
the way something is with respect to its main attributes	a politically organized body of people under a single government
a politically organized body of people under a single government	a political system in which the supreme power lies in a body of citizens who can elect people to represent them
the group of people comprising the government of a sovereign state	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 territory occupied by a nation	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 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)

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