The difference, as I understand it:  

A bump map takes information from a black and white extra map and applies a bend to the direction surface normals of the geometry are pointing.  This can "fake" the appearance of a raised or dented surface up to a limit.

A displacement map uses a simlar setup, but does not just tweak the normals, it actually moves the surface geometry by an amount indicated by the range from white to black on the map.  This is going to produce a more realistic roughening of a surface, likely at the cost of more computing power and render time.