scratch is more localized - smaller area. A scrape is more wide spread and skin is worn down & maybe bleeding. I scratched my foot on that rock while I was walking. I fell off my bike at speed and scrapped my knee.

I think so a cut is an open wound on the skin that occurs from something sharp, such as a knife. A scratch is lesser wound, typically a mark or very tiny incision, that occurs from something such as a fingernail or thorn. An abrasion is when the skin has been scraped hard enough to rub away

The tip of a dry ink pen will leave a scratch on the paper. The edge of a metal spatula can be used to scrape food off a cooking surface. Scratches are narrow and sometimes deep, scrapes are wider and usually on the surface.