Yes, Satin refers to the finish on the blade. Satin is slightly textured, in that there are 'streaks' of scratches, for lack of better description, all in the same direction. These scratches are very fine, and when looked at under the light, shine like satin. Each surface is uniform in it's direction of streaks. Black coating, as said above is applied over the naked steel, usually to protect it from the elements, and/or to reduce reflections. There is also bead-blasted and varying degrees of that. This is more of a dull appearance, which is a result of very tiny 'pits' in the blade steel, also very fine.
Another finish on steels is 'stone-washed' similar in effect as satin, but the scratches are all in random directions, resulting in a uniform appearance, similar to a stainless steel counter in a kitchen.
Now, Mirror polished is exactly as it sounds. Usually looks like chrome plating, but isn't. The naked steel has been so finely finished that there are NO scratches visible.
I'm sure there's a FAQ page somewhere that gives better descriptions.
Welcome to the Forums, by the way.
Daniel