Yes you are correct in that it is to fit a bowl or mug -However- grating certain soaps can make them lather much easier... ie: Mitchell's Wool Fat, Williams, TOBS... just to name a few of the Hard Milled soaps that now lather way easier in my collection...

If you gently and slowly melt the Glycerin based pucks using the double boiler method it is much safer then the microwave... Plus you only have to melt them enough to even out in the bowl they don't have to be completely liqufied..

Hope that helps...