How bright a surface appears in a render is determined by its angle to the light. A surface pointing directly at a light will receive more light energy than a surface turned away. The angle of a surface is stored as the normal vector, each face of a mesh has a normal and without any mapping the render engine will use this to calculate the output pixel intensity.

Bump and normal maps both generate detail by modifying the base normal of a surface using a uv mapped bitmap that overlays the base mesh. This allows the render engine to calculate a unique normal for each pixel of the bitmap giving the impression of higher res detail. The difference between the two is a bump map contains a height value that the render engine uses to modify the base normal where as the normal map contains a vector (XYZ = RGB) baked in when the map was generated.
Normal maps require software to generate, as already mentioned they are useful for transferring detail from a high res model to a lower res model. They are also specific to the mesh they were generated on, applying a NM from one figure to another can produce strange results.

For Firefly the level of detail may be dependent on the shading rate as textures are averaged across a micro-polygon. Try reducing the shade rate if the bump/NM looks lower res than expected.

Bump and Normal maps work on both diffuse and specular components of light unlike specular maps.

Displacement maps work by modifying the base mesh. Firefly breaks up the base mesh into micro-polygons before applying the displacement map so produce much finer details than Superfly.

Applying Normal maps there are at least two different formats, OpenGL and DirectX, they differ in the Z direction, if you find the relief is inverted it could be the wrong format. I use OpenGL which appears to work ok. Remember to set GC = 1 when applying the texture map.