
der Zettel
note / slip
A small, usually unlined piece of paper used for short notes, messages, or as a reminder.
Ich habe mir die Adresse schnell auf einen Zettel geschrieben.
I quickly wrote the address down on a slip of paper.
note / slip
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note / slip
A small, usually unlined piece of paper used for short notes, messages, or as a reminder.
Ich habe mir die Adresse schnell auf einen Zettel geschrieben.
I quickly wrote the address down on a slip of paper.

slip / ticket
An official or formal document on a single sheet of paper, such as a ballot paper, receipt, or parking ticket.
Heb den Kassenzettel gut auf, falls du die Ware umtauschen möchtest.
Keep the receipt safe in case you want to exchange the item.
The meaning depends heavily on the context. A 'Zettel' (note/slip) for a private note is informal. If the word consists of two parts, such as 'Kassenzettel' (receipt) or 'Strafzettel' (parking ticket), it is almost always an official document.
Ich habe einen Zettel mit der Telefonnummer auf dem Tisch liegen lassen.
I left a note with the phone number on the table.
When you write something down on a slip of paper, the preposition 'auf' is always used with the accusative. A typical reflexive construction is 'sich (Dativ) etwas auf einen Zettel schreiben' (to write something down for oneself on a slip of paper).
Kannst du mir deine E-Mail-Adresse auf einen Zettel schreiben?
Can you write your email address down for me on a slip of paper?
In its official meaning, 'Zettel' (slip/ticket) is often part of compound nouns. Important examples are 'der Kassenzettel' (receipt), 'der Strafzettel' (parking ticket), and 'der Stimmzettel' (ballot paper).
Er hat beim Falschparken einen Strafzettel bekommen.
He got a parking ticket for parking illegally.
message / news
Nachricht refers to the information being communicated and is not tied to a particular medium. Zettel, by contrast, refers to the small piece of paper on which a short piece of information can be written. When the content is what matters, Nachricht is appropriate; when the physical piece of paper is important, Zettel is appropriate.

Lea legte mir einen Zettel mit ihrer neuen Telefonnummer auf den Tisch.
Lea left a note with her new phone number on the table for me.
Lea schickte mir eine Nachricht mit ihrer neuen Telefonnummer.
Lea sent me a message with her new phone number.