Never heard of baking a specular before. Is that even possible?
Specular is a map that defines how light is reflected off a surface. A thumb print on a table will have less specularity than the areas surrounding it. It defines highlights.
Ambient Occlusion maps are NOT just used when dynamic lights aren't needed. That is a common misconception. Ambient Occlusion maps are almost always used, and in the case where their is in fact a dynamic light, they are used to bring out shadow details even further. Dynamic lights are not perfect, and it is sometimes hard to get the sharpness and realism that real life lights exhibit.
Bump maps change the surface normals across the object and change the brightness of the pixels based on the heightmap it's using. The surface normal then calculates how strongly the object interacts with light coming from any given direction. Bump maps lose their realism when you look at it from the side. Normal maps are the same as bump maps, but instead of using grayscale they use RGB to represent bumps giving it a wider range of data to use.
Parrallax mapping picks up where bump and normal maps fail and is an enhancement of the two. If you look at a bump or normal from the side, it losses it's depth. Parallax mapping is implemented by displacing the texture coordinates at a point on the rendered polygon. Thus, when viewed, has a more apparent depth.
A displacement map is a map that actually moves the geometric position of points, most often along the local surface normal, according the value on the texture map. It's more costly than the other types of maps though
And, if you wondering what the heck surface nromals are:
http://en.wikipedia.org/wiki/Surface_normal
I hope that clears things up
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