national capital vs metropolis

national capital and metropolis both are nouns.

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

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

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

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

national capital (noun)	metropolis (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