country vs city-state

country and city-state both are nouns.

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

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

country (noun)	city-state (noun)
a politically organized body of people under a single government	a state consisting of a sovereign city
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)