I'll try to shed light on the Hungarian part being an avid reader of early Hungarian history.

First of all it's important to see how your question comes from a confusion: As pretty much everyone knows, indeed the title prince (princeps) and duke (dux) are below the title of king (rex). But this is an European-Christian custom stemming from Roman use. European writers of course tried to apply their terms to other non-Christian rulers too, but the results were mixed and though they often got fixated over time (like calling the leader of Hungarians grand prince), its a matter of convention and does not recognize any sort of correlation between Christian and non-Christian ruler titles, or if there is any its often just incidental.

From this one can see that the idea that such a grand prince could crown themselves a king is silly since there was no higher title to them, and from their PoV the title rex (and even the eastern roman emperor, autokrator) was seen equal to them as being the highest leader of their respective people, exemplified by how Hungarians directly addressed these rulers in negotiations. One could hypothize a situation where a non-Christian ruler sees the title rex as higher than him and proclaim himself so, but such an act would have hardly been recognized by the Christian powers, most importantly by the Pope. It's little wonder why many Central and Eastern European states tie their foundation date to the crowning of their first Christian king, as this act was much more than a simple titular process.

Going into Hungarian parts specifically, we don't actually know what were Hungarian grand princes called. Early Hungarian history left us behind the following terms, recorded by Byzantine, Arab and German writers: megas archon, meaning grand prince in greek and an internal title that was applied to Hungarians by Constantine VII, supposedly the highest ruler, then Bruno of Querfurt called the highest leader magnus senior and said he stood above the other princes (leaders of separate tribes), gyula/gula/gila/dzila, the military and day-to-day leader, kende/kündü, sacral-spiritual leader, supposedly the other title of the grand prince and finally harka/horka/harkas, lowest title we know of (these latter ones recorded by both Greeks and Arabs, notably Ahmad ibn Rustah). We don't know if overlap existed, about how fluid these terms were, and what was the exact leadership structure like and how it may evolved over time. Historians have some ideas, a prominent one proposes that the relative certainity of persons known to be grand prince and other titles reflect the evolution and possible merging of titles until theres only one relevant title, the grand prince left by the late X. century, but the scarcity and confusion of records (later medieval Hungarian chroniclers seem to take these titles as being personal names for example) mean this may all be just a bias coming from our very impartial knowledge. We don't know if Christians at time understood the nuances and differences, as theres no relevant sources surviving, though it can likely be safely guessed that whoever had to deal with Hungarians had the necessary knowledge about whos in charge. It's possible the term grand prince was completely external and only used by non-Hungarians to disguingish between the many tribal leaders and other titles I outlined above.

In short, the term grand prince was a name used by non-Hungarians applying their own culture's names onto Hungarian leadership, but likely does not reflect the same sort of hierarchy as seen in Christian and other states, while the Hungarian titles themselves only partially survive with some uncertainity regarding their exact meaning, and for the highest actual leader (called grand prince in sources) there was no higher title to attain in their own culture.

During the Middle Ages, European textual sources from non-Christian sources are very rare, so it's worth mentioning at the beginning that almost all of our textual evidence for the period has to be interpreted through the lens of the largely clerical writers responsible for its recording, as well as the largely elite - both secular and clerical - nature of its intended audience.

It's also worth remarking on the material cultural differences between early medieval Scandinavia, early and high medieval Europe and Greece, and the contemporary Pagan Slavic world. While we lack pre-conversion literary sources from Scandinavia, we still have a rich archaeological legacy in the form of runestones, carved tablets and the like. While we can only acess Norse mythology through the lens of post-Conversion Christian authorship and we cannot read their contemporary stories, we can still see a glimpse of their everyday language and lexicon; this is something sadly lacking in early medieval Slavic studies. While early medieval Slavic sites have been excavated - and I recommend Dr Hajnalka Herold's work on hillforts - their physical contents are much less well known to us. One striking thing from Thietmar of Merseburg's detailed depiction of Wendish sites in his Chronicon is the extent to which everything is carved wood - a medium not famed for its archaeological survival.

A final point to consider is the nature of conversion. The conversion of Scandinavia to Christianity is a largely voluntary affair, spearheaded by Scandinavian kings to whom the accompanying socio-cultural symbolism and tangible literate bureaucracy attached to the Church are extremely desirable. In Eastern Europe, however, the conversion of the Slavs is largely down to direct German conquest or the fear thereof.

What's the point of all this rambling, you may ask? The sources from which we derive non-royal titles for Pagan Slavic rulers are part of a Christian narrative that we could term imperialist which directly seeks to delegitimise non-Christian rulership in favour of promoting the title of "rex" as an explicitly Christian ideal. St Stephen, for example, obtains his 'kingship' when he converts and is crowned by the Pope, as his new Christian title bestows the Romanitas and legitimacy of his new station on him. Bear in mind that it is quite likely that in local Slavic languages, the title used by these rulers did not change, or already bore the symbolism of 'king', but was deemed lesser or simply ignored by Christian contemporaries until the adoption of the Church and the concommitant arrival of Latin and of Church bureaucracy added the Latin Christian "rex" to a title. Because of the lack of sources, we just don't know what these rulers called themselves pre-conversion. Just as today, we also shouldn't overlook the sheer likelihood of things simply being lost in translation, and for Christian writers to give these individuals some kind of 'equivalent' title before they received their kingship.

An interesting note here is Poland. The Polish word for king is Król, which is a derivation of the Latin Karolus or Charles. This is because instead of Rex the Poles picked up on the Karolus used in Karolus Rex - better known as Charlemagne - signed at the bottom of Carolingian laws, decrees and letters.

In Scandinavia, things are somewhat different. The kings who spearheaded conversion would be keen to have themselves immortalised in a good light, so would take pains to make sure that they were 'rex-ed' retroactively. This may simply be a result of royal commissioning of histories which will thus of course strive to emphasise the power of their patron and his dynasty.