Every European country has different rules regarding feudalism; however, if we're willing to draw in broad strokes, we can construct a fairly regular feudal hierarchy.

The necessary condition is that the King, say, of France in the year 1050, cannot rule all of the kingdom on his own. So he divides it among his friends. This largest feudal subdivision is a Duchy. In France, the traditional duchies were Burgundy, Normandy, and Aquitaine (plus the Archbishop of Reims who for all intents and purposes also ruled a duchy). In England prior to the Norman Conquest, this rank was called "Earl", while in Germany, he would be called "Herzog".

Of course we could get into the gritty details and point out that prior to the Carolingan Conquest Burgundy and Aquitaine had been independent kingdoms up to the ninth century; but that has more to do with their individual history than the "broad strokes" feudal hierarchy I'm outlining. Further, yes the ruler of Brittany, once annexed by France, was demoted to the title of "Duke". Conceivably if/when a larger kingdom annexed a smaller one the territory would be re-designated a Duchy, but that's not the "intended" role of the Duke in the feudal system.

A Duke in the year 1050, in turn, cannot conceivably rule his entire Duchy on his own, so he splits up the territory among his friends (and ideally, family. They try to kill you less, sometimes). This second subdivision is called a Country, ruled by a Count. The Duke of Normandy, for example, split up his Duchy in the counties of Rouen, Meulan, Evereux, Eu, Contentin, Cau, Bayeux, Avranche, Aumale, and Alençon. The Counts, in turn, would split up their counties among Vice-Counts who would in turn, split their territory among Barons.

Of course, there are weird exceptions to this rule. Some Counts didn't have Viscount-level subdivisions, dividing their territory among Barons. Most had a mix; one or two large Viscounts, and a half dozen Barons. Some counties, like the County of Toulouse, didn't even belong to a Duchy, being directly under the rule of the King (and in the case of Toulouse, the King later ruled it directly as his own possession from the thirteenth century on). Further, several Counts under the direct rule of the King who had either by purchasing or marrying (or even sometimes war) acquired large, near-Duchy sized territories were elevated by the King to the rank of Duke (Bourbon, Orleans, Anjou, Berry, Angoulême, Alençon, Touraine).

There are also Marquis, which are technically on the same level as Dukes but rule border territories. Thus they have more responsibilities, but also more rights (this title is also present in Germany as "Magrave").

It gets really fuzzy when you move out of the middle ages to the early modern period, when sovereigns as a whole worked to reduce the rights of the nobility, eliminating rights that allowed them to "rule" and making them resemble something closer to modern "ownership", dissolving the bonds that tie Counts holding their titles under their Dukes and so forth.

So to finally answer your question, yes sometimes annexed kingdoms were demoted to Duchies, however that is not the intended role of a Duke. Indeed, EUIII makes a multiple mistakes because of this mechanic: if, say Tuscany, follows the historical path and changes government from Noble Republic to Constitutional/Absolute Monarchy, it will be called "Kingdom of Tuscany". This is not accurate; technically Tuscany was a Duchy-level subdivision of the Holy Roman Empire. An independent Tuscany, then, would be a Grand-Duchy; a title still in use by the modern state of Luxembourg, which came to become a similarly autonomous part of the Empire.