ritzen
to scratch
To cut or engrave a superficial, narrow line or scratch into a surface.
Er ritzte seine Initialen mit einem Messer in die Baumrinde.
He scratched his initials into the tree bark with a knife.

to scratch / to cut
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to scratch
To cut or engrave a superficial, narrow line or scratch into a surface.
Er ritzte seine Initialen mit einem Messer in die Baumrinde.
He scratched his initials into the tree bark with a knife.

The meaning changes completely depending on whether the verb is reflexive or not. 'Sich ritzen' (to self-harm by cutting/scratching oneself) almost always refers to self-harm, while 'etwas ritzen' (to scratch/engrave something) describes engraving or scratching a surface.
Sie ritzte ein Herz in den Sand.
She scratched a heart into the sand.
When engraving or scratching a surface, the structure 'etwas (accusative) in etwas (accusative) ritzen' is often used. The first accusative object is the sign or mark, and the second is the surface.
Die Kinder ritzten ihre Namen in den alten Holztisch.
The children scratched their names into the old wooden table.
The reflexive form 'sich ritzen' (to self-harm by cutting/scratching oneself) is a very serious and sensitive term from the field of psychology. It describes a form of self-harm and should be used with care.
Psychologen helfen Jugendlichen, die sich ritzen.
Psychologists help teenagers who self-harm.
to cut
'schneiden' and 'ritzen' both have to do with a sharp object. 'schneiden' is more general: you divide something, shorten something, or accidentally injure yourself with a knife or scissors. 'ritzen' more often means making a narrow, superficial line or a scratch in a surface. With skin, the difference is important: 'sich schneiden' often happens by accident, while 'sich ritzen' can mean intentional self-harm. Learners may confuse the words because both describe an injury or mark made by something sharp. A simple guideline is: deep or dividing is more likely 'schneiden'; superficial and line-shaped is more likely 'ritzen'.

Der Schlüssel hat eine dünne Linie in den Tisch geritzt.
The key scratched a thin line into the table.
Beim Kochen habe ich mich mit dem Messer in den Finger geschnitten.
While cooking, I cut my finger with the knife.