What do you use to rub food into small pieces by moving the over a certain tool?

You're describing the process of grating.

The tool used for grating is a grater. Grating involves rubbing food against the rough surface of a grater, creating small pieces.

There are various types of graters, each with different sized holes, for creating different textures:

* Box grater: A common type with different sized holes on each side, allowing you to grate cheese, vegetables, and more.

* Microplane grater: A fine-mesh grater, ideal for zesting citrus fruits and grating hard cheeses.

* Rotary grater: A handheld grater that uses a rotating drum with sharp blades.

* Cheese grater: A specialized grater designed specifically for grating cheese.

Let me know if you'd like more information about any specific type of grater!