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The visual difference between bump mapping and displacement mapping: areas in direct light are fairly well represented by a bump map, but the bump map approximation fails at oblique angles, where actual occlusion matters more.
GIF
And here's a slight better comparison that isolates the effect of the geometry by making the displacement similar in scale to the pseudo-displacement implied by the bump map, as well as using an Oren-Nayar reflectance model to reduce the unrealistically bright highlights.
GIF