In PM,
Material refers to the material that pixols are getting painted with. Like rgb, they are indexed numbers. For example flat color is 0, and fastshader is 1. so with this option on, you can embed different materials into 1 texture map. If this special multi-material texture is exported as a PSD, the different materials will be different shades of grey in the alpha channel, for use in rebuilding materials in another app.
Shaded refers to the final rendered look including lighting, shadows, and any other render options, even fibers. be careful when using the shading option, as it can result in over bakeing your object when used a few times. IOW, shading on top of shading. To aviod this, paint a flat color over the areas you wish not to shade.
BTW, the word you were looking for was “Shaded” not shader. Quite different.