They overlap in meaning. They're not exactly the same and not completely different. Sometimes they're synonyms.
"Bang" emphasizes the loud sound, usually a sharp, surprising sound. It suggests something strong. It suggests an explosion, a crash, and serious damage.
"Bump" emphasizes the physical shock. "Bump" usually suggests something mild. A soft collision, followed by the two objects bouncing away from each other. If you think of it as making noise, you think of it as a "dull thud," not a "bang."
You can say "The drummer bangs the drum" but you can't say "The drummer bumps the drum."
You can say "there was a loud bang from the firecracker," but not "there was a loud bump from the firecracker."
If you are in a plane and flying through rough air, you might say "We hit a lot of bumps," but not "there were a lot of bangs."