Greece vs Balkan country

Greece and Balkan country both are nouns.

Word	Noun	Adjective	Verb	Adverb
Greece	Yes	No	No	No
Balkan country	Yes	No	No	No

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

Greece: ancient Greece; a country of city-states (especially Athens and Sparta) that reached its peak in the fifth century BCE
Balkan country: any one of the countries on the Balkan Peninsula

Other hypernyms of Greece include Balkan nation, Balkan state.

Greece (noun)	Balkan country (noun)
a republic in southeastern Europe on the southern part of the Balkan peninsula; known for grapes and olives and olive oil	any one of the countries on the Balkan Peninsula
ancient Greece; a country of city-states (especially Athens and Sparta) that reached its peak in the fifth century BCE