They're not opposites.  As I understand it, the difference is where zero level is.  On a bump map, black is flat, or even with the surface.  White is above the surface.  There is no below the surface.  On a displacement map, 50% gray is even with the surface.  White is above the surface, black is below the surface.  hth. :-)

One goes into the house of eleven eleven times, but always comes out one. -River Tam