It seems to me that you are more or less asking what the concept of the nation state makes it different from other forms of statehood. In that case this thread might be of interest of you: Some historians talk about the "rise of the nation state" in the 16th-17th century, but what elements made these states different from previous states?.

It's also important to note that even when nation states did form, people within these states didn't necessarily identify with that state in a very strong sense and more or less had a stronger connection with the region they lived in. Basically, the nation state shifted the concept of statehood from an area controlled by a sovereign to that of an area belonging to "a people". This is a rather impactful change as with the former borders shift as kings die and areas under their control don't always end up under the same ruler. The concept of a nation state on the other hand solidified borders as the people within are a determining factor of what the state is.

As you can imagine, this wasn't a process that did happen overnight, and you can easily argue that various countries already had a much stronger sense of nationhood before the concept of a nation state did catch on. Also, the way the nation state concept was picked up by different countries/rulers was not in a uniform way. What you however see is a shift of responsibilities where the government at national level started to take on other duties and passing different kinds of law. A very noticeable one is instituting education from a national level. Which does make sense as with education you effectively can also create a stronger national identity. People, more often than not, spoke regional dialects that would be difficult to understand from other regional dialects not that far away. So educating people in a single language does help in communication. But it also gives people a connection in the form of that language. The same is true for history, it more often than not found itself part of the national school curriculum in the form of a nation building tool. Which is the reason that in many countries still history in schools isn't history in a broad sense, but history focussed on the country itself and even then the more heroic events and the big events that showcase the shared history for that country.

You can also see differences in how strict countries enforce these sorts of things. France for example, effectively took the position that French is the only language to be spoken and very nearly succeeded in eradicating other languages spoken before the process of forming a unified nation state began. That's not to say there aren't any regional differences anymore in France, they are however (as far as language goes) not as pronounced as they would have been 200 years ago.

There is much more to be said about the subject. Unfortunately, I have ran out of time to expand on it for now and I only have partially answered your answer as I can't expand on China historically as my knowledge there is not enough. I do however hope that my answer has given you some more context around the concept of nation states.