provincial capital vs city

provincial capital and city both are nouns.

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

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

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

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

provincial capital (noun)	city (noun)
the capital city of a province	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