The problem here is that all of these terms are in some sense Eurocentric. I don't say that as an epithet: it's factual. They're tied to the history of the Mediterranean world and Western Europe.

"Prehistory" makes some degree of vague sense in that it describes a period of time that we know existed after the appearance of Homo sapiens sapiens where we have some evidence of the distribution of human populations and the movement of humans to more and more areas of the planet and some evidence about the development of language, of technology/material culture and the coming of the Neolithic and settled agricultural communities. But even there, what we mean by prehistory differs considerably based on what part of the world we're talking about, both in terms of what we know and in the time periods we're referencing.

"Ancient history" tends to be understood as Greek and Roman history. Even within the eastern Mediterranean, it could and should also mean the history of Persian, Mesopotamian, Egyptian and Ethiopian states/empires--the use of Greek city-states and the Roman Empire to define "ancient" or "classical" history is strangely selective. One could speak of "ancient" in reference to societies on the Indian subcontinent, in East Asia, in Southeast Asia, in West and East Africa and Oceania, but it doesn't entirely work--and it implies a kind of developmental sequence that is simultaneous with and comparable to the Near East and Western Europe, when in fact what you might call "ancient" happens at different times and carries on for different durations in different parts of the world.

It's past that point that the scheme really breaks down. "Medieval" or "Middle Ages" is so specifically tied to Renaissance Europe's sense of coming out of period "in between" the Western Roman Empire and the Renaissance. It is in some sense Renaissance propaganda. It simply doesn't make any sense anywhere else except that everywhere else was also "in between" whatever was "ancient" and the coming of modernity. Historians of non-Western societies tend to grit their teeth if they absolutely have to use an "era" marker to help readers understand where they are in time in relationship to European history, but mostly we know it's just not relevant or helpful to talk about "the medieval". If there is an era or epoch label worth using that is relevant, it's usually regionally specific--it can't be used more widely. (Think for example of dynastic periods in Chinese history.)

"Modern" makes sense because it is global and relational and even the Eurocentrism of it works somewhat because it is a period defined in part by the rising power of Western Europe over the emerging world-system after 1500.