In the real world, there is specular vs diffuse (a few other things to but anyway).
Time for a lesson in quantum mechanics.
The concepts of specular and diffuse reflectance are based in quantum mechanics and the wave-particle duality of matter (in this case, light).
A quantum of light, known as a photon, is diffusely reflected if it is absorbed by the material and emitted. This uses the wave properties of light. Because it is a wave, the direction in which it is emitted is indeterminate. In essence, the photon is emitted in all directions. Hence, a diffuse reflection does not depend on the angle of view; the same quantity of energy is emitted in all directions, so the view direction is unimportant.
Because the photon is absorbed and reemitted, the photon is emitted with a different wavelength (color) than the one that was absorbed. Technically, many photons of varying wavelength are emitted. The particular wavelengths of photons emitted depend on the properties of the material. What we see as the color of the material are the wavelengths of the color that are being emitted by the surface. Note that not all of these wavelengths are in the visible range, even if the incident light was in the visible range.
Specular illumination comes from a different interaction. Rather than being absorbed and emitted, a specular reflection comes from a photon literally bouncing off of the material. Now, some materials (metals in particular) do have some effect on the color of specularly reflected photons. But, in general, the color of a specular reflection is based on the color of the incident light.
Note that the presence of one does not necessitate the lack of the other. These are independent concepts that have effects in independent ways.
The “texture” of a surface (roughness) determines ultimately how mirror-like the surface is (the dot(N, H) ^ k term tends to take this into account for Phong illumination). There are other factors that determine the strength of the specular reflection (typically taken into account by the OpenGL specular color of the material).
A surface cannot be described simply by giving a percent diffuse, and therefore the percent specular is 100 - that percent diffuse. It is just not that simple.
A surface that is prone to diffuse reflection can still have specular interactions. In fact, most surfaces that you see as being purely diffuse have quite a bit of specular characteristic to them, which is one reason why lots of rendered surfaces (especially in games) look very fake. Though it may be hard to consciously see the specular reflections, you expect them, and miss them when you don’t see them. The specular characteristic to human skill is one of the reasons that making rendered humans is so hard.
Lastly, these two interactions are all you need to determine how a surface interacts with light. The diffuse term is pretty trivial; the standard OpenGL diffuse works just fine. It’s the specular term that’s the horrible pain. I’ve seen very large equations that only give approximations (good enough to get movie-quality graphics, but still approximate) to reality.