I don't understand the confusion over this and desert flying. Sand in the desert is made of large grains of silica. They are rounded from years of abrasion and they won't have the same melt characteristics of the finer, sharper mica in the ash cloud, which being fine will melt more readily, will be deflected less by airflow direction changes (coating more of the engine interior) and being more abrasive.
The abrasion characteristics are rather similar actually. Most W. Oz jet aircraft ended up with painted leading edges, to stop the sand abrasion making holes in the leading edge - that's how bad the problem is.
The real difference, apparently, lies in the melting points.
.