I can only offer a partial answer...

In the cultural orbit of the Byzantium, and especially the Slavic world, "Caesar" initially spread because Byzantine emperors conferred the title as a mark of prestige (and subordination) on various allied rulers. This practice, first attested in 695 (when Justinian II granted it to Khan Tervel of Bulgaria) became less common from the reign of Alexius Comnenus onward, when the more spectacular title "sebastokrator" came into use. By then, however, "Caesar" (Tsar) had become entrenched as a mark of prestige.

Bulgarian rulers proved especially fond of the title, partly because so many sought to dominate or conquer Byzantium.

The grand princes of Kievan Rus, by contrast, never made "Tsar" part of their official style, preferring to reserve the title for individual rulers remarkable for their strength or wisdom. After the Mongol conquests, the "Tsar" was the Khan of the Golden Horde. Ivan III's assumption of "Tsar" as an imperial title was both an appropriation of this custom and an expression of the claim that his kingdom was the natural heir of the Roman/Byzantine Empire.

In the west, "Kaiser" was the standard German title of the Holy Roman Emperors from the coronation of Otto I (962) onward. I'm not sure, however, why it was chosen over some variant of "Augustus." The prestige of the man Caesar probably had something to do with this title becoming standard (though the Commentaries were not yet widely read). It may be that no clear distinction was seen between "Caesar" and "Augustus" in terms of prestige, since both were associated with imperial rule.

I hope another reader of this thread will be able to expand on the connotations of "Caesar" in the medieval German world.

Sources

Federica Rossi, "Caesar as a political title" in A. Grafton et al. (eds.) The Classical Tradition (Harvard UP, 2010), 159-61

Oxford Dictionary of Byzantium, s.v. "Caesar"