country of origin vs country

country of origin and country both are nouns.

Word	Noun	Adjective	Verb	Adverb
country of origin	Yes	No	No	No
country	Yes	No	No	No

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

Other hypernyms of country of origin include land, state.

country of origin (noun)	country (noun)
the country where you were born	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)