Or is there any? For instance, I'm researching Mesopotamia and the Near East, and I saw references to the Early Dynastic Period of Mesopotamia, and then when I switched the Near East (Transjordan area), the term Bronze Age was used more often, even roughly with the same dates (3300/3000-2100/2000). Is there any difference between the terms or are they used interchangeably?
Age, period, era, and the more colloquial "times" are basically interchangeable--it's a matter of convention more than anything else.
A good example is, we say Middle Ages, but "medieval age(s)" sounds wrong whereas "medieval period" or "medieval era" sounds fine. Well, medieval is just medium (a)evum: literally, middle age. (It's more apparent in older English when it's spelled mediaeval). So medieval period is middle ages period. Absolutely equivalent, just preference.
For instance, I'm researching Mesopotamia and the Near East, and I saw references to the Early Dynastic Period of Mesopotamia, and then when I switched the Near East (Transjordan area), the term Bronze Age was used more often, even roughly with the same dates (3300/3000-2100/2000). Is there any difference between the terms or are they used interchangeably?
Ancient Near Eastern historians and archaeologists use "ages" as chronological markers that allow cross-cultural comparisons. "Periods," on the other hand, refer to region-specific political developments.
For example, the Late Bronze Age spans ca. 1600-1150 BCE across the eastern Mediterranean. Within the LBA, scholars speak about the "Kassite period" and "Middle Assyrian period" in Mesopotamia, the "Hittite empire period" in Anatolia and Syria, the "Late Palace" and "Post-Palace" periods in Crete, the "Middle Elamite period" in Iran, and so on. Within the Middle Bronze Age (2000-1600 BCE), there's the Old Babylonian period in Mesopotamia, the Old Assyrian period in Anatolia, the Sukkalmaḫ period in Iran, the Middle Kingdom and Second Intermediate Period in Egypt, etc.
The Oriental Institute has a helpful timeline.