developing country vs nation

developing country and nation both are nouns.

Word	Noun	Adjective	Verb	Adverb
developing country	Yes	No	No	No
nation	Yes	No	No	No

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

developing country: a country that is poor and whose citizens are mostly agricultural workers but that wants to become more advanced socially and economically
nation: a politically organized body of people under a single government

Other hypernyms of developing country include body politic, commonwealth, country, land, res publica, state.

developing country (noun)	nation (noun)
a country that is poor and whose citizens are mostly agricultural workers but that wants to become more advanced socially and economically	a politically organized body of people under a single government
	the people who live in a nation or country
	a federation of tribes (especially Native American tribes)