A 'Grand Duchy' isn't just one type of thing!

European countries (inc. Russia) have never had a unified system of Monarchy and Nobility. Traditions vary depending on which time period and which territory you're talking about.

To further complicate matters English has a habit of applying 'Grand Duke' quite liberally to translate positions of senior nobility in other languages which we don't have direct translations for. For example Russian distinguishes between 'Prince' as a courtesy title and 'Prince' as a substantive tile.

English therefore has used terms like 'Grand Duke' or 'Grand Prince' to reflect this distinction when talking about Russian nobility, but there's no consistently applied rule for how one translates from one language/system to the other.

It doesn't make any sense to directly compare the Kingdom of Denmark to the Duchy of Moscovy as if they're supposed to fit in to some neat system.

it's like asking why the British Prime-Minister isn't called 'President' or why the German Chancellor isn't called 'Chairman'

Different countries, different languages, different traditions.

DIVERSITY!

I can't speak about Lithuania, but in the case of the Muscovy it was because of Orthodoxy. Orthodox rulers have no "Kings" per say except in some particular examples when the orthodox ruler levitates between Constantinople and Rome (Serbia, Bulgaria). The first slavic Orthodox state was Bulgaria and as the pagan Khan Boris converted in 864 he took the title Knyaz (Duke), which was considered the equivalent of a catholic King. Therefore, despite the equal translation of Knyaz and Duke the titles weren't equal in the catholic and orthodox worlds. When his successor, Simeon expanded Bulgaria to include most of the Balkan peninsula and other nations, he took upon himself the title Tzar, which was to be equivalent to the Byzantine Emperor. Thus Tzar is not supposed to be regarded as the orthodox King, but rather the orthodox Emperor.

Muscovy was therefore a Dutchy only in the sense of the etymological translation that occurred - Knyaz = Duke. However in reality an orthodox Knyaz was considered equal to a catholic King and thus Muscovy was in fact an orthodox Kingdom. It only became Tzardom when it united most of the lands of the ancient Rus and regarded itself as "The third Rome", thus taking an imperial title, which is what a Tzar is.

In the case of Lithuania i could argue the same applied since the country was in fact in its vast majority an orthodox state. Only the tiny, baltic part we call today Lithuania and back then Zmudz and Samogitia were ethnically Lithuanian and Pagan/later Catholic. The entire rest of the country, including today's Belarus, Ukraine and parts of Russia were inhabited by slavic, orthodox people, who also contributed vastly to the Lithuanian aristocracy. Therefore, i suppose the same orthodox principle applied of Knyaz (translated in english as Duke) equal to a King and a Tzar equal to an Emperor. In this sense both Lithuania and Muscovy were only through a mistake in translation "Duchies" but in reality considered by their orthodox inhabitants equal to catholic Kingdoms.

Ps. Sorry for the long post, here's a modern Belarusian song where the people sing about their own country as being "Litwa" (Lithuania) and the Belarusian people as being Lithuanians : https://www.youtube.com/watch?v=YHwbUx7SGbs

Grand Duchy in Russian would be "Velikoe knyazhestvo", from "knyaz'", i.e. Prince in this scenario. Slavic "knyaz'" is a cognate of king or konung in English or Scandinavian languages. It doesn't help that Russian knyaz' could rule a small town or a large multi-region domain. In other countries there was a distinction between counts and dukes and kings. In Rus, not really... "Velikiy" or "Grand" was first applied to ruler of Kiev, but then princes of Chernigov, Vladimir and others start using the title as well.

So, what I am driving at here, while English language translates "Velikoe Knyazhestvo" as Grand Duchy, it meant entirely different thing in Russian, a kingdom, if you will. Rulers of Muscowy certainly felt equal to Danish Kings, whatever the title.

Would these denominations have been chosen by the rulers of the times? If so, is it possible that there would not have have been uniformity across Europe? Would the name-choosing thus have been arbitrary?

It is a bit complex. Muscowy was not a Grand Duchy as such. Rather, it was a Grand Principality - the title is related to the German Fürst. However, in English literature, the orthodox princes are translated as dukes and grand princes as grand dukes to reduce the confusion with a son of a monarch, which would also be called prince.

However, the German Fürst and Furfürst are translated as prince and prince-elector, so it gets confusion.

European royalty were from the time of Charlemagne recognised as royalty by the pope. Portugal and Hungary became Kingdoms by the approval of the pope.

At the time when the title Grand Duke of Lithuania and Grand Prince (or Grand Duke) of Muscowy were created, they were not under the influence of the catholic pope. Lithuania was pagan, and Muscowy was orthodox.

The Scandinavian monarchs had a long tradition of calling themselves Kings - in fact, there were a multitude of Petty Kings - this is why three crowns is the national emblem of Sweden - it was formed by uniting the three petty kingdoms of Svealand, Västergötland and Östergötland.

When German missionaries started arriving in Scandinavia in attempts to convert the pagans there from the 800s to the 1100s, they realised the easiest way was to convert the leader and then have him convert his people. Flattering the local leader by agreeing to his claim to be King was an easy way to be on his good side.

Thus priests and monks would carry letters from bihops and archbishops to the Scandinavian Petty Kings, who were at the time more or less forming their Kingdoms by defeating other petty kings and refer to them as "Rex" (King in latin).

There was a long tradition of having someone called King, and the church simply played along. There was no such tradition and no catholic church to play along in Lithuania or Muscowy.