There is no simple and easy answer to that, since you can look at almost every individual title and find an individual answer for that.

Empires:

Since you are only referring to european titles, I'll ignore the other traditions (China, Persia, Muslim and more), since those are their own beasts to wretle with.

I'll start from the top, so let's talk Empires. Looking at medieval europe, there is the conception that there can be always only one emperor. This has several reasons, but to dumb it down, it finds it's roots in the tradition of the Roman Emperors (mainly Konstantine the Great) and in the duality of Pope-Emperor. One was responsible for the matters of Faith, and the other one for the earthly affairs. (This is, of course, only the theory. In reality there were endless conflicts between the pope and the Emperor)

In the west, basically the catholic world, there was the Holy Roman Emperor, who was, in nomine, senior to all others monarchs. The reality was often different, but this is not important here. The first one was Charlemagne, crowned by the Pope.

All Holy Roman Emperors claimed their tradition from him, and he claimed his tradition from the Roman Emperors + the sacral element added by the pope. After Napoleon, who disbanded the Holy Roman Empire, the tradition splits. We have Napoleon himself, who crowned himself an Emperor (old Roman tradition + revolutionary tradition), Josef of Austria (continuation of the old Holy Roman tradition, now limited to Austria) and later Victoria and the German Empire. (Victoria was Empress of India, and the germans had the old Holy Roman Tradition, mixed with nationalistic innuendos + prussian militarism).

Now to the eastern (orthodox) tradition, which also goes back (oh wonder) to the roman emperors. Technically, the title of the Roman Emperor never vanished in the east, since the Byzantine Empire was the greekified continuation of the Eastern Roman Empire. (The Byzantines called themselfes Romanoi, which I don't need to translate).

(And yes, I know the debate about calling it the Byzantine Empire, but for simplicity I'll gonna roll with it.)

Before Charlemagne, a lot of the 'Barbarian' Kingdoms, founded in the old Western Roman Empire pledged (nominal) alliagence to the Byzantines.

The tradition splits again. Mainly to the Bulgarian Czardom (derived from Ceasar, the family name of Gaius Julius Ceasar, later used as a title.) and later one to the Serbian Czardom (Which I openly admit, to not know a terrible lot about. Balkan History was always a bit.... messy.)

After the Fall of Constatinople, the Princes of Moskow, fellow orthodox christians, claimed the tradition through faith and marriage to the last Byzantine dynasty. The Czardom of Russia was established. (Idea of Third Rome).

(Note, that the conquerors of Konstantinople, the Ottomans, also claimed the imperial tradition.)

So, to wrap up the European Empires, you'll notice several trends. First the claim of the tradition to the Roman Empire (how wacky it may be, it was a must have.), second the aspect of christian faith.

The western tradition clearly splits with the eastern tradition, but it serves it's point.

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Kingdoms:

Now, here it get's somewhat messy. Kingdoms derive in western europe from the old tribal structures. Note, that Kingdom does not mean Kingdom. We have a plethora of Kings in Ireland, for example, which noone else bothered to recognize. We have the Anglo-Saxon Kingdoms in England.

(I would say, that the British Islands had the highest rate of Kings per capita in the whole world.)

You notice, that the most important thing about being a King is not to have something you call your Kingdom, but have everyone else recognize you as a King.

Here is also one aspect of your question. A King can be a vassal an Emperor, but he does not need to be. This brings us to the one big thing which is linked to your question and the medieval world in general feudalism.

Feudalism is an evolution of the old tribal structures and a very complex thing in it's nature. But it is the reason for your question. It is in itself a toppic for a whole field of study, but its consequence is, that a King can be a vassal of a Emperor, but he does not need to be. Simiraly a 'Duke X'

and a 'Count Y' can be both vassals of a 'King A', but the 'Count Y' does not need to be a the vassal of the Duke 'X'. But there can be an another 'Count Z' who is a vassal of 'Emperor B' along with 'King A'.

Confusing? Yes, very much so. But important here.

And this is only the theory. 'Count Z' could be more influential and powerful than 'King A'. This was rare, but could happen. If you understand this, you also are able to understand the full medieval experience.

Let's continue with the royal traditions.

Let's start with the French and German Kingdoms.

(Yup, there was a German King through most of the Middle Ages.)

The french Tradition goes back to the old Frankish (Germanic) Tribal Kingdom. Established by the Merovingian Dynasty, which was later replaced by the Carolingian Dynasty, from which Charlemagne hails from (The founder was actually Charles Martell).

After the Death of Charlemagne and his heir, Louis the Pius, the Frankish Empire, was devided to Western Frankia, Eastern Frankia and Middle Frankia. (Threaty of Verdun)

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