The Babylonians were later than the Sumerians. iirc, the Sumerians got conquered by the Akkadians, and then the Akkadians evolved into the Babylonians. Sumerians used cuneiform as a written language; the Akkadians spoke a Semitic language (like Hebrew or Aramaic but different from Sumerian); cuneiform script and Akkadian language blended together and that’s what the Babylonians used.
Also, these were cultures spanning like 1,000 years and large areas, so there are going to be a lot of differences. The religions are similar in broad strokes—the Hebrews’ religion also fits into this mold. The Babylonians apparently preserved and adapted Sumerian myths, especially the Epic of Gilgamesh and the flood story within it.
They all believed in astrology, that the world had a certain shape (flat with a solid-dome sky), and thought the gods lived in the sky, but the head god changed. For a while the head god was Enlil, but the Babylonians around 1400 BC changed the head god to Marduk. (The Hebrews, in turn, changed it to their god, Yahweh).