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
Loading your saved state.
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.

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.
card / map
'die Karte' and 'der Zettel' can both be small pieces of paper or cardboard. The difference lies in their purpose and material. A 'Karte' is usually sturdier and often has a specific function, for example as a postcard, playing card, or credit card. A 'Zettel' is usually a simple piece of paper for a note, a short message, or also a single official piece of paper such as a receipt. You can confuse the words if you only think about the shape. The important point is: a 'Karte' is more like a finished item for a specific purpose; a 'Zettel' is more like paper with brief information on it.

Kannst du mir die Adresse auf einen Zettel schreiben?
Can you write the address down for me on a slip of paper?
Zum Geburtstag schreibt Anna ihrer Freundin eine Karte.
For her birthday, Anna writes her friend a card.