When someone just talks about shaders without specifying, which one are they usually talking about?

The demo from the reading looks similar to the same thing without custom programmed shaders, are there things we can change to make it look different by changing the shaders?

The clipping planes example shows only one new triangle, what's the second one mentioned in the caption? Also, what's the effect of the geometry being modified in this way and is it something we should take into account?