[pradn]

A nation is a body of people that believe they are similar (usually ethnicity or language.) "An imagined community".

A state is the entity that taxes people, builds roads, maintains a military. It has a "monopoly on violence" in a particular territory.

A nation can be stateless - like the Kurds or Uyghurs. They have a cohesive self-identity, but lack their own state. Colloquially, "nation" can also mean "country" - think "national champion", but this more specific meaning exists as well.

It's rarely necessary to use the term "nation-state". Just using "state" is fine. I suspect people like using it because it has a nice ring to it and sounds serious.

[SAI_Peregrinus]

The USA has 50 states, none of which are nations (and thus not nation-states), but which together comprise the whole nation-state union. So the US government and US institutions tend to use "nation-state" more often than others do, because it's a useful disambiguation for them.

[pradn]

That makes sense but I think it should be possible to tell that a "state" refers to another country, not a US subfederal unit.