Scrape (correct spelling) is more of a surface injury. Cut is deeper.

I was walking and fell. My knee hit the concrete sidewalk. I scraped my knee. There were a few drops of blood. I washed it off and put a bandage on it. It healed right up. I was using a knife in the kitchen. I slipped and cut my finger. The cut was deep. I had trouble stopping the bleeding. I wrapped tape around it and put ice on it, then I went to the hospital emergency room and they put stitches in it.

scrap = лом cut= вырезать