national capital vs city

national capital and city both are nouns.

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

As nouns, city is a hypernym of national capital; that is, city is a word with a broader meaning than national capital:

national capital: the capital city of a nation
city: a large and densely populated urban area; may include several independent administrative districts

Other hypernyms of national capital include capital, metropolis, urban center.

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