In specular reflection, light rays bounce off the surface of an object at the same relative angle that they approached it. In diffuse reflection, light rays bounce off in many directions.
For example, under normal conditions a rooftop has a matte surface which reflects the light diffusely. The rooftops in the painting on the left show diffuse reflection on a dry, sunny day. The sketch on the right shows slate rooftops after a rainstorm. The thin surface of water remaining on the rooftops now reflects the light more specularly.
“Speculum” is Latin for mirror; the rooftops in the second sketch do act more like a mirror, revealing reflections of the dark chimneys.
Many surfaces are a combination of specular and diffuse reflections. When you polish a shoe or an apple, what you’re doing is increasing the relative proportion of specular versus diffuse reflection.
Whether you’re rendering digitally or traditionally, you can think of the specular pattern as a separate layer added on top of the usual form-modeling factors that you would use to render a matte object. In the 3D realm, surface modelers have to consider the normal modeling factors that you would study on a plaster cast plus the specular effects.
More about specular and diffuse reflection on David Briggs' Huevaluechroma.com
Wikipedia on specular reflection
"The Physics Classroom" on the comparison, with diagrams
Previously on GJ: Shadows vs. reflections on water.