Territory works better. States are not unincorporated.
Territory implies we actually own the territory directly in US politics.
It stands as this in levels of how much they are part of the US:
military Occupation: American zones of Austria and Germany and all of Japan after WW2. Obviously, this is military occupation.
Protectorate: Cuba and Panama(effectively. Had someone attacked them, the US would have into full war with the aggressor or at least give panama a $@&$ ton of help. More likely would have directly intervened.) this is closest in function to a vassal. Phillippines I think might have also been one.
Commonwealth (different from UK definition.) and Uncorporated organized territory: Guam, Puetro Rico, The virgin islands, and the Mariana Islands. Puetro Rico and the Mariana Islands are US commonwealths, so they have a higher standing than the other two. This is the first level were one has US citizenship. This is also the second level that America owns directly.
Incorporated Unorganized territory: this level is the level of stuff owned by America, and thats the only relation it has. It includes up to 12 miles out at sea, many atolls, AND ALL
US ships. Military and civilian. Though the military ships technically are far more organized...it's called discipline. The first level the US owns. Note: US owned shop implies it has been registered in the US. It does not need be owned by an American.
Incorporated Organized Territory: hawaii before it was a state...this is one of the bigger lists, as most the states were made from territory in this category ( as in the territory was this level at time of statehood. Some states however were formed before they made it this far. California is one of the most noticeable, having managed to gain state hoodnin the course of only a few years from when we obtained it.Texas went directly from being a nation to being a full state. ) the other term for this is Territory. This is why calling a vassal a territory is incorrect, as the player would not even own said nation. These regions are fully part of the nation, more than Puetro rico is, and are also organized.
State: most places, state means the nation. In the us, it means the first level fully and completely part of the US. Even then, they have many powers typical of a nation, in fact the only one they don't have is Rights to diplomacy, and to negotiate treaties among the rest of the nation. The states have a right to maintain militias though, so they are allowed militaries though.
Counties: sub division of a state. A logical extension of federalism applied at the level of the state.
The Feds: The federal government: the glue that makes the 50 states not effectively 50 nations in alliance. Congress, the executive branch, supreme court, the military, CIA, FBI, DIA, the bureaucracy. This is what handles disputes between states. And they have the right to diplomacy and they own the full military, including the militias during times of war. They used to be less powerful, but because most domestic trade has a hard time not crossing borders for any of the needed parts of getting to a consumer (even food, as that fertilzer had to come from somewhere, just that place could be some where not in state.), the feds could more easily push the states around using their constitutional right o regulate interstate commerce. For example, if a state does not require a person be 21 years or older to buy achohol, The feds withdraw 5% of the needed for funding transportation for that state. It worked. Mostly because they gave states that much funding for passing said laws, meaning it was a good idea to do so so they could fund thing easier.
all in all, Protectorate is what we must go with for American vassals. Terriotry implies we own the place directly. commonwelath does to. State simply can not work, for obvious reasons. protectorate implies said protected nation is independent territory wise and government wise. Which they are as a Vassal state