Typology and the cause of difference between European medieval kingship?

The feudal structure in place over the bulk of Western Europe devolves from the structure put in place during the Carolingian dynasty. The structures of authority created at this time were blessed by the Pope, forming the basis of Divine Right of Kings.

Charlemagne in particular created a pattern of Stem Duchies (and Marches) throughout the empire. These were to become substantial regional power bases for the respective ducal dynasties, but tempered by a universally acknowledged concept of an over-riding royal authority, and vassalage.

In France an initially very weak royal authority evolved into a rather strong nation state by the end of the Hundred Years War in 1453, perhaps partly as a direct consequence of it. The corresponding developments in modern Germany and Italy would not occur until 400 years later. Ironically, Royal/Imperial authority in the German region was initially much stronger, but faded rapidly over time.

Similarly in Iberia, initially a number of stem-kingdoms (Castile, Aragon, Leon, Navarre & Portugal) independently arose as Muslim rule there faded. By what appears to have been deliberate arrangements by those dynasties, a consolidation occurred by 1492 with Spain as a personal union of (Greater) Castile and Aragon and only Portugal remaining distinct.

Although Britain was never under Carolingian Rule, the conquest of England by William I in 1066 was followed by a complete remaking of English feudalism in the contemporary Continental model - with improvements. William distributed the estates of all his Tenants-in-Chief through the entire kingdom to prevent the possible development of regional power bases. Only the Stanleys and Percys seem to have been able to build any sort of true regional power base.

None of this structure or history occurred in Eastern Europe or Scandinavia, leading to a system of common arrangements between equals in forming national polities. Thus elected monarchs.

Pieter Geerkens gave a good answer on feudalism, but missed the mark with the conclusion that the elective monarchies appeared from areas that were not part of the Carolingian Empire, because of a lack of feudalism.

Of course, both East and West Francia elected kings. Hnece, the answer to this part of the question:

In Poland and Hungary kingship was not hereditary, but elective. Why this difference?

Is that it's actually not as different as you might think. Most, if not all, of Europe's major crowns were originally elective.

To start with, the power to elect Roman Emperors was vaguely understood to be vested in the Senate. When the Western Empire finally fell, the Roman Senate sent an emissary to Constantinople to "basely renounce the right of choosing their own master, the only vestige which yet remained of the authority that had given laws to the world". Nonetheless, hereditary succession was never truly enshrined in the Byzantine Empire either.

More generally, Germanic kings are well known to be elected. With the migration of Germanic tribes, elective kingships thus proliferated. Harold Godwinson was elected by the Witenagemot to succeed Edward the Confessor as King of England in 1066, as did Edgar Ætheling. Swedish kings had to be elected by the Mora Thing. Denmark maintained elections for her kings until 1660.

In the heart of Charlemange's empire, the Kings of West Francia became elected after the Carolingian Empire was reunited under Charles the Fat. This continue through to Hugh Capet's election and beyond, though royal power rendered it a formality and the institution died a quiet death after a couple of centuries. The Kings of East Francia, later Holy Roman Emperors, however remained elective until the Empire was dissolved in 1806, possibly to prevent Napoleon's election.