Height Map vs. Normal Map

Both can bake from high poly to low poly but the difference is...

Height- Deals with tesselation, which is taking a mesh and subdividing it) changing the height of the mesh but not its collision

Normal- Fake lighting to create the appearance of height without changing the mesh.

height- tesselation ( take a mesh and subdivide it) changes the actual height of the mesh (does not actually have collisions, you can also make landscapes out of it) normal- faking lighting to create the appearance of height