Pumice is coarser grit than Rottenstone, bit they are different materials as well.
Pumice is a volcanic rock. That light weight one that floats on water..
Rottenstone is a mineral, I think a type of limestone.
The latter can be ground/milled down to finer grades as well.
Some finishers start with Pumice for the project and then switch to a final rub down with a favoite grade of rottenstone depending on how high of a gloss they desire.
Most of the commercial rubbing compounds for polished metal & finished wood & painted surfaces have (or at least had used) some small amt of rottenstone in them as the polishing agent.
The finest grade was used in glass polishing/lens polishing so it can be quite fine
It can actually enhance a gloss and bring it up on a surface rather than 'knock it back' when you get to the finest grades.
Good 'ol Brasso brass polish has a touch of rottenstone it in to brite polish the brass surface. That along with ammonia compound to remove the brass oxidation.
...Don't use it on a Shellac wood finish (like a Stock) as the Ammonia will disolve the Shellac..