Country: The land not within a city. It can also mean "nation". Village: A small settlement. Rural: Something in or from the country, rather than from the city. Rustic: Something in the style of being old-fashioned or rural. As for words for settlements, we have "village", "town" and "city". The difference between these is the number of people living there.

Just a note about a city. It's not just about the size, at least in the UK. Having a cathedral and a royal charter from the monarch can make a small population centre into a city. The smallest city is the UK is St David's with a population in 2011 of 1,841. https://en.wikipedia.org/wiki/List_of_smallest_cities_in_the_United_Kingdom

Thank you for your comment. And it was new to me word "hamlet". Before I thought it was name of Shakespeare's character. Now I know that is also a settlement less than village.

As nouns the difference between village and country is that village is a rural habitation of size between a hamlet and a town while country is (label) an area of land; a district, region. Source: https://wikidiff.com/country/village