What is the difference between roughness and specular in the Principled BSDF shader?

If you turn up matallic all the way you can see what roughness does: it’s the difference between a mirror and something like lead or pewter. Non-matalic materials with very low roughness include smooth plastic or polished wood which you can see a bit of a reflection in.

Yes, roughness is a good thing to put a smudge map on if your dealing with a very smooth surface.