Hugo B. answered 08/16/22
2D/3D Animation & Character Rigging w/ 5+ yrs of experience w/ Blender
It's simple to differentiate between the three really.
Bump maps are greyscale textures you map onto objects to create the illusion of surface relief (elevations & depressions) on an otherwise flat object. With this type of map, the depressions & elevations appear/look real since they don't truly alter the geometry of a surface which is what happens with Displacement maps.
Normal maps are a type of transfer map. This means the texture is created from a polygon object. There are distinct types of transfer maps which handle the conversion from polygons to textures differently. For example, a normal map captures the surface normal information of the source mesh and uses it to light the targeted mesh.
Displacement maps are grayscale textures which one maps onto objects in order to create true surface relief (elevations & depressions) on literal flat objects, The perfect example of this type of map is how it is used to create terrain maps for animations and even game environments rather than manually modeling the entire world terrain (think of maps like GTA and all the shooter games with large maps for sniper's).