country vs countryside

country and countryside both are nouns.

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

As nouns, countryside is a hyponym of country; that is, countryside is a word with a more specific, narrower meaning than country:

Other hyponyms of country include back country, backwoods, boondocks, hinterland, farming area, farmland, scrubland, weald, wold.

country (noun)	countryside (noun)
a politically organized body of people under a single government	rural regions
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)