der Schlitz
slot / slit
A long, narrow opening or cut in a surface, for example in a mailbox, a machine, or a piece of clothing.
Wirf die Münze bitte in den Schlitz des Automaten.
Please drop the coin into the slot of the machine.

slot / fly
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slot / slit
A long, narrow opening or cut in a surface, for example in a mailbox, a machine, or a piece of clothing.
Wirf die Münze bitte in den Schlitz des Automaten.
Please drop the coin into the slot of the machine.

The meaning of 'Schlitz' (slot / fly) becomes clear from context. If people are talking about machines, mailboxes, or walls, it means a narrow opening. In connection with trousers ('die Hose'), it means the opening at the front.
Der Brief passt nicht durch den schmalen Schlitz.
The letter doesn't fit through the narrow slot.
In the meaning of 'Öffnung' (opening), 'Schlitz' is often combined with verbs of dropping something in or pushing something through. Typical examples are 'eine Münze in den Schlitz werfen' (to drop a coin into the slot) or 'einen Zettel durch den Schlitz schieben' (to push a note through the slot).
Für ein Ticket müssen Sie drei Münzen in den Schlitz werfen.
For a ticket, you have to drop three coins into the slot.
The discreet notice 'Dein Schlitz ist offen' (your fly is open) is a very common and useful phrase in everyday life. It is used to point out to someone that the zipper on their trousers is open.
Ein Freund hat mich leise darauf hingewiesen: „Du, dein Schlitz ist offen.“
A friend quietly pointed it out to me: 'Hey, your fly is open.'
cut
'der Schnitt' and 'der Schlitz' can both describe an opening created by cutting or separating something. 'Schnitt' is more general and can also be an injury or a cut place in a material. 'Schlitz' usually means a long, narrow opening, often with a specific function, for example in a mailbox, in a machine, or in clothing. Learners may confuse the words because a 'Schlitz' can be created by a 'Schnitt'. The difference is: 'Schnitt' emphasizes the action or place of cutting, while 'Schlitz' emphasizes the narrow opening.

Steck den Brief bitte in den Schlitz am Briefkasten.
Please put the letter into the slot on the mailbox.
Beim Schneiden von Gemüse hat Tom einen kleinen Schnitt am Finger bekommen.
While cutting vegetables, Tom got a small cut on his finger.