A NATION
A nation is a settlement of homogeneous clans which originated as families. I assume as clans used to roam about, they would encounter ethnic territories or lands where they would settle among. The roving clans may intermarry within the larger nation & become part of it. Multiethnic "nations" or empires are typically a Eurasian ideal than an African one & came with increased population & improved modes of travel. What centralises a nation is usually feudal chiefs, a monarch, a faith/belief system or simply physical features of an individual (genetics) & language. A nation, by default, is a usually - at best - a country because it's land & thus it's borders are typically known by other regional clans & nations. A nation with no land typically become roving clans among other nations or are constantly in conflict with the imperial power that aims to annex their land.
A COUNTRY
A country is a state with centralised or consolidated authority. An empire made of many other nations & states can be an country. What centralises a country is politics or documents. A country's land (or borders) are commonly demarcated on a map. A country cannot exist without land it can defend or exist on.
In brief; a diverse country (linguistically or ethnically) is more commonly referred to as a "state", "country" or "empire" & a more ethnically homogeneous country is often called a "nation"
(N. B.: A homogeneous empire is still a nation.)
A nation is more a homogeneous people regardless of which political structure they are under & a country is more often a political structure governing a land. So while you can call the USA, South Africa, Belgium, Nigeria, DRC, Kenya, Australia & India "countries", they are not nations.
This may or may not be associated with the above but here's something interesting to know:
Country in Zulu is "izwe" & inhabitants of an izwe are "isizwe" (a nation). Nation & country having the same etymological origin in the language. Indicating that in the Zulu world a nation & country used to be one & the same thing.
In Latin languages, peace & country seem to have a similar etymological origin indicating a country is a land where citizens can live in peace. The assumption then is if people can't live with each other in peace, it's not a country.