Bump map is usually used to create some illusion of small height differences while a displacement map is used to actually displace geometry and create real height differences in the model (can be done with a geometry modifier or a shader depending on the program used)
Note that for displacing geometry you need more faces in the model to actually get resolution enough to get the height difference and details, your displacement map should also preferably be 16bit gray levels so you get enough height information to get the subtle details translated in the displacement of the geometry. The extra tessellation of the model can be done at render time with the settings provide in a displacement shader.
In case of a displacement modifier you usually place a tessellation modifier in between.
