The bulk of material in classic stone carving -- including soapstone -- is done with chisels and a mallet. Stone chisels are quite different from woodcarving chisels. In fact, they really don't cut the stone. It's more of a controlled break. Some of the chisels called "point chisels" are like ice picks, removing larger chunks of stone. Once larger areas have been removed, rough surfacing is done with chisels that have a sawtooth shape. They are called "claw chisels" and they are similar to a row of several fine-point chisels. Eventually, the chisels closely resembled cold chisels and do finer surfacing and shaping.
Once large-scale removal has been done with a point chisel and mallet, and finer surface shaping has been done with other chisels, rasps and files come into play. Stone rasps are very similar to files; they are just coarser. They are each used to file away stone, smooth and contour the surface of the sculpture to a finer degree than chisels. Rasps and files are handwork, unlike the mallet work of the chisels.
Sanding is yet another finer step. In the sanding process, some shaping can still take place. Stone is being removed. But, less shaping and more surfacing is taking place. The primary difference in this technique is that sandpaper or emery paper is not stiff like chisels and rasps; they take on the contour of the stone. You can apply pressure through the paper to the stone.
Polishing is essentially fine sanding. Polishing (and even sanding) are not required. It depends on the final surface you want to create. Often, some areas will be sanded and polished and others will be left rough. Emery paper is ideal for soapstone because the substrate is cloth and cloth contours, whereas paper tends to tear and wear out. Also, a wet sandpaper is advisable. Small amounts of water can be helpful to to lubricate the wet sanding and polishing process.