Mesopotamia is the ancient Greek name for the land between the rivers, the Euphrates and the Tigris. This geographical location is more or less modern day Iraq. The ancient Sumerians of Mesopotamia was one of the earliest political powers in ancient Mesopotamia, they were since replaced by the Akkadians, who in turn were replaced with another people. The Babylonians was at one point also a regional power in the area, though not contemporary with the Sumerians.
The reason why Sumerian, Mesopotamian and Babylonian mythology being used interchangeably is that they in many ways worshiped the same gods and told the same myths. There is good evidence for seeing the political and cultural landscape of Mesopotamia as one culture that evolved continuously up until the Persian and Macedonian conquest of Mesopotamia. Though there were changes in the gods they worshiped during the millennia and the myths they told, several of the stories and gods can be found in archaeological remains from the earliest civilization of Mesopotamia as well as in writings.
So to answer your questions, the Sumerian, Mesopotamian and Babylonian mythologies are used interchangeably, and can be hard to differentiate from each other, as they in many ways are just slightly different versions of the same myths and gods.
Mesopotamian mythology is used to reference all the mythologies of the region, ranging from Sumerian, Babylonian, Assyrian, etc.