It is counterproductive to try to apply that local vernacular meaning of the word "nation" to understand the term "nation state", which describes a particular kind of state that is different from other kinds of states. It will only confuse you. It would be like trying to understand the term "laser cooling", which describes a refrigeration process, by using the vernacular meaning of the word "cool" that is "in fashion". Please see https://en.wikipedia.org/wiki/Nation_state.
But that particular "vernacular" is important, and not only because American audience has a large presence here on HN, but also because it is influential and is imported into other world languages - one example being the term "national park" which has nothing to do with a nation-state (or a park, for that matter) but simply means what should be easily expressed in any language as "a state nature preserve."
The "in fashion" meaning of the word "cool" is also important and influential (and imported into other world languages!) but it is not the relevant meaning in the phrase "laser cooling". At best you can say that the American audience has a propensity to be confused about the term "nation state", compounded by its general historical illiteracy.
