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)