When I taught first year International Relations one of the early lectures covered the difference between state, country, and nation. Although used interchangeably by politicians, in IR the state is a political structure of which there are only about 200 in the world, mostly recognized by other states as being such, and with the legitimate recourse to the use of force (plus a couple of other factors). A country was a geographic reference - think Wales or the Basque Country, or Switzerland because a country and a state can share the same geography (and often do). A nation was not about political organisation or geography but a shared identity - sometimes ethnic, sometimes religious, sometimes nationalist - between a group of people.
Hence the US could be a single state and country, while being inhabited by many nations (American, Sioux, Apache etc). The UK could be a single state made up of multiple countries and inhabited by people identifying as members of many nations.
And occasionally you'll have a case where you have a distinct nation that has a well defined country (say Tibet) but is not recognized as a state.
> the state is a political structure (...) mostly recognized by other states as being such, and with the legitimate recourse to the use of force
What makes it legitimate, except that other states will recognize it? The status quo.
This is why China can crack down on HK, or Spain on Catalonia.
In a sense, it is not much different from organized crime: gangs recognize each other, sometimes fight but most of the time stay within their borders, and exert violence to punish their members that deviated from the rules. The gang members recognize that the use of violence to punish fellow members is legitimate.
In practice, most states recognize all other states. There are exceptions (Israel lacking recognition from some states, a few edge cases owing to long-ago treaties etc) even if they don't have good relations. The US and Iran, for example, might not have diplomatic relations but they both recognize the other as existing.
In some ways it is a little arbitrary. A new state like East Timor or South Sudan can be declared and immediately recognized by most everyone, and then admitted to the UN. Kosovo can déclaré itself a state, be recognized by a lot of other states, but lack a seat at the UN and 'real' statehood. And then there's a case like Taiwan which does more or less everything a state would or could do...but is recognized by almost nobody.
While it's not perfect, a good rule of thumb as to whether a state is really a state is if they are full members of the UN. It's not perfect - the Holy See and Switzerland were non-member states for a long time - but it's close.
In reality, it seems that those rules are bound for a change. UN at large needs to recognize that the current nationalistic movements are not going to die out, and go back to the core goal of preventing violent conflicts, which current arrangement is anything but helping.
I am not sure what the solution is, but providing a predetermined cost for separation of a part of the country is a simplistic framework that might work.
Eg. Catalonia gets their independence, owes Spain ~20 billion euros over the next 20 years, and they each guarantee to each other that it will not raise taxes to opposing products in the next 30 years[1]. For Kosovo it's a bit late to avoid violence. But as state separation becomes common and accepted as "normal", there will be less of "this is terrible" storylines that politicans thrive on, so harder to pull people into violent wars.
Oh well, one can only hope. FWIW, I am sure that will lead back to unification efforts (you know, to share costs and optimise development: eg. it's hard to design a good railroad if you are governing only your tiny county), but as long as we define clear uniting and separating guidelines, I hope we can reach acceptable terms for all parties.
[1] Not saying this is a fair arrangement, but I am sure there could be a way to define something that is fair and probably written onto thousands of pages :)
So you'd say West Virginia is a country but not a state, and every Chinatown is a nation? I don't think your definitions match the accepted reality in the American English language.
A tract of land; a region; the territory of an independent nation; (as distinguished from any other region, and with a personal pronoun) the region of one's birth, permanent residence, or citizenship.
Hence the US could be a single state and country, while being inhabited by many nations (American, Sioux, Apache etc). The UK could be a single state made up of multiple countries and inhabited by people identifying as members of many nations.
And occasionally you'll have a case where you have a distinct nation that has a well defined country (say Tibet) but is not recognized as a state.