a stiff piece of material with a section of Carborundum cloth, wrapped over it,
[sand paper for metal, on a cloth backing]

Can be used to remove metal , with a back and forth motion
by hand.

a file only cuts in one direction, like a saw.

abrasives are able to cut back and forth.

Like sandpapers, by increasing the grit number the grit is finer
and so makes surface smoother.