British vs country

British and country both are nouns.

Word	Noun	Adjective	Verb	Adverb
British	Yes	Yes	No	No
country	Yes	No	No	No

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

Other hypernyms of British include land, nation.

British (noun)	country (noun)
the people of Great Britain	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)

British (adjective)	country (adjective)
of or relating to or characteristic of Great Britain or its people or culture