I don't even know if "scratch" applies to both cases:
I slice a (slightly) harder object on a (slightly) softer surface. It leaves an inwards scratch. The harder object is not damaged at all, but some material from the softer one is lost or merely displaced. Ex: a putty knife on putty, or a metal object on a potato, etc.
I slice a softer object on a harder surface. It leaves a mark on the harder object, and the softer one "grinds" thus getting slightly damaged. Ex: Chalk on a chalkboard, a metal knife on a porcelain dish.
So, what should word these phrases?
- The putty knife made a __________ on the clay block.
- The knife made a __________ on the porcelain dish.