Part-2 is really where I cover what is going on under the hood of the renderer. http://www.cineversity.com/vidplaytut/the_physical_renderer_-_part_2
The Sampling subdivision is more or less your base subdivision through out the scene, this value affects anti-aliasing along the edges of objects and also DoF and Motion Blur.
The Shading subdivisions mostly affect surface effects such as textures, blurry reflection/refraction and AO.
A pixel is always going to be an averaged result of all of its subdivisions.
so in stage a we have an image that is of a blue sphere and a smaller yellow sphere.
The resulting image will be 1px by 1px.
in both the top and bottom the pixel has subdivisions, the top fewer than the bottom.
in column b) the objects have filled the subdivided areas edge to edge based on how much of the object resides in that subdivision.
in column c) the result from b) is averaged out to display a pixel to us.
Although we started with the same initial scene the divisions change what values get averaged to provide the final result.
And from help file, why does upping the shading subdivision min and max have no effect if the sampling subdivision is zero.
I’m not to sure where this is from, raising the values in the shading/min/max will cause changes, but can only produce results that are somewhat clean, you need to still raise the sampling subdivision to get the best results.