Normal Maping is a type of Bump mapping and the most common type you see today. Normal Maping is applying a texture with a per pixel normal that you use to calculate the lighting of fragments. This lighting trick makes it appear likes bumps. Bump maping can be other things though like Enviromental Maping which is were you have a texture which the red and green channels hold texture cooridnate offsets which is usually used to sample a texture holding a reflection of the enviroment. So as you can imagine its usually used for bumpy reflections.