city vs state capital

city and state capital both are nouns.

Word	Noun	Adjective	Verb	Adverb
city	Yes	No	No	No
state capital	Yes	No	No	No

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

city: a large and densely populated urban area; may include several independent administrative districts
state capital: the capital city of a political subdivision of a country

Other hyponyms of city include national capital, provincial capital.

city (noun)	state capital (noun)
people living in a large densely populated municipality	the capital city of a political subdivision of a country
a large and densely populated urban area; may include several independent administrative districts
an incorporated administrative district established by state charter