Kurdistan doesn’t really have a central government like that, nor fixed or well defined borders. Keep in mind that the concept of a “Nation State” is really only a couple hundred years old.
If that counterexample doesn’t satisfy you, then Somalia should. It is a country without a functioning government, which has two nations inside of them of the northern and southern Somalians which are completely different, and neither of which have any sort of unifying government.
That’s your point though, isn’t it?
The “people” and the “territory” are not the same thing, but both words “country” and “nation” are used more or less interchangeably to apply to either.
The words country and nation are absolutely not interchangeable, no matter how lay people use the terms.