As far as I’m aware, Normal maps are a hybrid of Bump and Displacement maps.
Bump map(greyscale)…gives the effect of displacement but is only a “2d” effect to give the impression from the camera angle. It cannot change the mesh and so the “silhoette” of the object won’t change.
Displacement map (greyscale)…actually deforms the mesh at rendertime.
Normal map (multicoloured)…It creates an effect similar to bump maps except it also has information to change in the Z axis from the mesh. Red=info to change in the x axis, Green= info to change in the y axis, Blue= info to change in z axis.
In effect perhaps this means that Normal maps will eventually take over from Displacement maps…when it’s more supported by 3d programs.
This is all my impression, so anyone correct me if it’s wrong.