By "societal system," I don't mean feudalism, communism, etc. There's 3 "states" with their own borders that form 1 nation on the same continent. They have different governments and councils, yet they share the same culture, religion, and laws. I'd like to add a title to the 3 of them that form a single nation. I was thinking of using alliance, but it's more than an alliance, really. Nor can I call it a federation. What would be a title for the states. The name of the country is Vauk.
Holy crap, now that you say Kingdom, I remember having that idea. I just forgot. It was the Holy Kingdom of Vauk
If Vauk is a kingdom, presumably it has its own king and overall government. Which would make the three states within it in song kind of feudal subordinate relationship. So you could go with a name from European feudalism, to keep things simple--maybe they're duchies or counties? Or to be more exotic you could use some of the less well known feudal names--the Holy Roman Empire was divided into "circles", for instance. Or go with a non-European name, but I'm not as familiar with those.
Actually, feudalism plays such a large part in that world, it's just outside of the main land and is applied to the Lesser Lands. Kingdom works fine. There is a King, but there is also a council for economic means.
The closest thing to come to mind would be the Holy Roman Empire. An overarching Emperor over the German princes and petty kings. But, also, by the end of the Empires days the Emperor was basically a figurehead, with all of the power with his vassals. Which creates a interesting decision for you. Someone has to have all the power in this nation of yours.
The Shattered Sea trilogy by Joe Abercrombie (Half a King, Half a World, Half a War) deals, ultimately, with three kingdoms (united in tradition, divided over who they think should be superior and who subordinate) and how they share power. Joe's solution (no spoiler - read it yourself!) has a definite feeling of Realpolitik.
Normally this would be called a confederation. Someone said confederacy earlier and that's technically correct although that term is loaded in the American Civil War context. Since you have three, and depending on whether there are real religions in your world, you might toy around with the word "trinity". That literally means three entities that are distinct but form a cohesive whole - it's also loaded in all sorts of fun spiritual ways that may work to the advantage of a narrative.
I'm slightly confused why you can't have a federation but can have a confederation (since they are exactly the same thing) That aside other options might be a league (as in the league of nations - the foreruner of the UN), and alleigance , a council , or a play on trinity or triumvirate or simply the 3
They're not. Federations have much stronger central governments than confederations do, though the component states still have some amount of sovereignty.