From a techniques point of view, grinding, rasping and sanding are similar operations. In fact the Rasp is often considered the roughest of the sandpapers, preparing a tough or rough surface for subsequent sanding but it is also capable of some true grinding, like for removing thin-set mortar or grinding graffiti off of concrete.
What is unique about the oscillating tool is that it is capable of removing the toughest of thin set mortars and sanding wood down to a polished finish, but is not considered a tool for large surfaces. In fact it is the compliment to other heavy duty material removal tools, getting into the corners, edges and other tight spaces that the larger tool cannot do -- or handling the small job that the other tools can't fit into -- like cleaning up for the replacement of a single tile.
Here technique and dust removal are key. I have divided this video into 4 sections to make it easier to go to what you want to review:
1) Introduction plus Grinding/Rasp work; 2) Sandpaper grits; 3) Flat Sanding; 4) Profile Sanding.