When you rasp, you either file wood with a metal tool, or you speak in a harsh, irritating voice. Your rasp-y voice might get you a gig as a lounge singer, but probably not as a preschool teacher.
The tool called a rasp is a special kind of wood file that's much coarser than sandpaper, and when you use it, you rasp. If you've ever cared for a horse's hooves, you may have also used a rasp to file them. The "speak gratingly" meaning of rasp comes from the "scraping" sense of the word. If your voice sounds like a rasp against a rough surface, you're rasping.