Interesting question.
To the OP's question: unglazed ceramic is different from glazed. Glaze is basically clay with more silica added thus the glassy finish.
Clay is also made up of silica and alumina. In commercially prepared clay, like in an art studio, clay is formulated many different ways. Porcelain is the smoothest and fired to the highest temps, while there are rough finish stonewares used for sculpture that contain refractories, mainly fired clay crushed up, at different sizes to create texture.
There is also industrial ceramics, something I know just a little about, that involves stuff like restaurant use ware, ceramic insulators, etc. This clay is porcelain based but is more like a paste.
I haven't seen the recipe's for that kind of clay, mostly proprietary, so I can't comment on what the make up is. I do remember that it is different from my studio clay and it is fired at a higher temperature (there are three main different studio clays all fired at different temps).
Now, different surfaces, grit if you may.
Clay again contains refractories, tooth we call it, usually sand or fired clay that has been pulverized back to small particles measured by how it passes through a screen. Commonly called a 'mesh size.' For instance, a clay is 60 mesh if it contains refractories that can pass through a 60 hole per inch mesh screen.
The components that clay is made up of, or formulated with, are measured in mesh size also, typically 300 so they are all powders. I know you can order say, silica in meshes smaller than 300 so I think using different sizes of these components creates a different surface feature in the clay. You would think that when you fire it all together it would all melt nicely but that's not the case. You can make smooth or rough clay. Porcelain is the smoothest and typically the purest.
Long to short, clay is not clay and that's how you get different ceramic surfaces.
The problem is lapping the clay to get it flat. I would probably use stoneware as a medium grit and then porcelain as a fine.