city-state vs country

city-state and country both are nouns.

Word	Noun	Adjective	Verb	Adverb
city-state	Yes	No	No	No
country	Yes	No	No	No

As nouns, country is a hypernym of city-state; that is, country is a word with a broader meaning than city-state:

Other hypernyms of city-state include body politic, commonwealth, land, nation, res publica, state.

city-state (noun)	country (noun)
a state consisting of a sovereign city	a politically organized body of people under a single government
	the people who live in a nation or country
	the territory occupied by a nation
	an area outside of cities and towns
	a particular geographical region of indefinite boundary (usually serving some special purpose or distinguished by its people or culture or geography)