der Kratzer
scratch
A superficial, usually line-shaped mark or damage on a surface, caused by a sharp or rough object.
Ich habe einen tiefen Kratzer im neuen Parkettboden entdeckt.
I discovered a deep scratch in the new parquet floor.

scratch
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scratch
A superficial, usually line-shaped mark or damage on a surface, caused by a sharp or rough object.
Ich habe einen tiefen Kratzer im neuen Parkettboden entdeckt.
I discovered a deep scratch in the new parquet floor.

'Der Kratzer' (scratch) is the noun related to the verb 'kratzen' (to scratch). The noun describes the result of the action: when a cat scratches, it leaves a scratch.
Pass auf, dass du mit dem Schlüssel keinen Kratzer in die Tür machst.
Be careful not to make a scratch in the door with the key.
To describe the location of a scratch, German usually uses the prepositions 'in' or 'auf' with the dative. 'In' is used when the damage is in the material, and 'auf' when it is on the surface.
Nach dem Parken war ein neuer Kratzer in der Autotür.
After parking, there was a new scratch in the car door.
Scratches are often described more precisely with adjectives such as 'tief' (deep), 'leicht' (minor), or 'oberflächlich' (superficial). Common verbs are 'einen Kratzer haben' (to have a scratch) or 'einen Kratzer machen' (to make a scratch).
Es ist nur ein oberflächlicher Kratzer, den kann man leicht wegpolieren.
It's only a superficial scratch; it can easily be polished out.
cut
'der Schnitt' and 'der Kratzer' can both be a line on the skin or on a material. 'der Schnitt' is usually deeper and is caused by cutting, for example with a knife or a sharp edge. 'der Kratzer' is more superficial and is caused by rubbing or scraping, for example with a key, a branch, or a cat's claw. The words are easy to confuse because both can look like a line. If something is really cut into or open, 'Schnitt' fits. If only the surface is damaged, people are more likely to say 'Kratzer'.

Am Wochenende entdeckte Tom einen Kratzer an seinem Fahrrad.
Over the weekend, Tom discovered a scratch on his bicycle.
Der Schnitt in der Hand musste im Krankenhaus genäht werden.
The cut on his hand had to be stitched at the hospital.