So this whole thing is a kingdom. Now, right over here, this is a duchy, and a duchy will be controlled by a duke. I guess they didn't call it ducky because that just doesn't sound as serious. So the king might grant a duchy, a duchy to a duke, and in exchange, the duke would provide loyalty, pledge their fealty. If the kingdom is threatened, the duke will fight alongside the king, would provide their own troops. If the king wants to go conquer other territories, same thing, and also provide the king with taxes, which might be in the form of coinage, depending on what time and region we are in the Middle Ages, or it might be in the form of a percentage of the agricultural production from this duchy. Now, the terminology here is that the duke would be one of the king's vassals or would be vassal to the king.