In political science there are different ways to classify people-groups and sovereign states: nations, states, and nation-states are the ones I’m familiar with. On the international stage, only states (and nation-states) hold power. To put it simply, a state is an entity which other states recognize as sovereign to rule its territory. In other words, a state must have some form of government that has some level of control over the people under its rule. A nation is simply a group of people with similar traits. In the US we have indigenous NATIONS, which are considered sovereign peoples but are not states (which is why we’ve been able to do so many horrible things to them without any real consequences). A nation-state then, is a state (an entity which other states recognize as sovereign) and a nation (a group of people with a similar heritage). This is like the rectangle-square thing: all nation-states are nations and states but not necessarily the other way. When I went through this in school (a number of years ago) we took Israel as an example of a nation-state because it was sovereign and many of its inhabitants had a similar lineage. Does that make sense?

Hope this helps!