I hear some people refer to the outside of some natural stone as the natural surface face and sometimes people call it rough-back. What is the difference?

The terms mean the same thing. Some materials have traditionally been referred to one way or the other, but they mean the same. Many times rough-back refers to the natural staining from the sedimentary layers on the surface of white limestone or lueders. Granbury stone is traditionally a material where the outside of the stone is referred to as natural surface color.