I should let Nick or the other masters answer this but am also curious....
Figure I'll give you my answer and we'll see who chimes in to correct or add to my understanding.
Types of finishes.
Mirror Finish - the steel is brought to a mirror polish, I.E. you can see yourself. This can be done by hand or machine. By hand it is done by advancing through grits up to 1,000 and higher. Hand polishing compounds are often used after the last sandpaper grit. Machine polish usually means a buffing wheel. Like hand sanding you progress through grades of polishing compound to get the finish you want. See methods below. Not a very durable finish but required to bring out the hamon on a blade that has one.
Satin finish - blade is finished to a lower grit level than a mirror polish. The advice here on grit is good. Try them and go with what you like. The streaking or scratches on a satin finish should follow the length of the blade. Folks often polish to a grit higher than the target finish to give a smoother foundation for the final grit. The blade is then final polished at the lower grit. This gives a more consistent finish. Satin finiahes are more durable in use than a mirror polish.
Acid finish - the blade is polished to at least a satin level and then given a patini using some kind of acid. Can be a consistent gray shade or a mottled patinia. Google the methods there are lots of them. The patina offers some corrosion protection on a carbon steel blade.
Stone wash - the blade is given an initial polish and then put into a tumbler with some kind of abrasive media (lot of choices here). The blade comes out with lots of random scratches. Again, Google the methods. I've read where folks do this in a washing machine using a padded coffee can. That would'nt fly on my house

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This method is best reserved for stainless blades. The scratched surface retains moisture and promotes corrosion more than mirror or satin finishes.
Sandblast finish - the blade is sandblasted after initial polish. Again, best reserved for SS.
Methods of finishing.
Hand finishing - just like it says. The polish is done largely by hand. Depending on the methods it can give a more consistent and smooth finish than buffing. A buffer will not remove any peaks or valleys left from grinding. It will mask them but won't completely remove them. A buffed blade "can" have more waviness than a hand polished blade. But like many things, it all depends on the craftsman. A buffed blade from one maker may be much more consistently smooth than a hand polished blade from another.
Machine polish or buffing - After grinding is complete, for me thats around a 220 or 320 belt, the blade can be buffed to finish. There are mutliple grades/"grits" of compound and they change by manufacturer. The main supplier has a web page that describes the differnent compound. I can't remember the website or company name.. The coursercompounds can throw sparks and really remove material.
I just recently started buffing and now wonder why I held off.... Unless I am doing a hamon, I now hand sand to smooth at a lower grit, 150 or 220, remove any inconsistencies from grinding and then go to the buffer. You do get rounded corners and edges but keep that in mind and plan around it where you want crisp edges on the knife.
I would guess most folks probably use a hybrid method of both hand and machine polishing methods.
Barry