
der Brief
letter
A written message, usually written on paper and sent by mail in an envelope.
Ich habe heute einen Brief von meiner Oma bekommen.
I got a letter from my grandma today.
letter
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letter
A written message, usually written on paper and sent by mail in an envelope.
Ich habe heute einen Brief von meiner Oma bekommen.
I got a letter from my grandma today.

vehicle registration document
Colloquial short form for the vehicle registration certificate, the official document that identifies the owner of a motor vehicle.
Für die Ummeldung des Autos brauchst du unbedingt den Brief.
For re-registering the car, you absolutely need the vehicle registration document.

official document
An official certificate or administrative document that establishes certain rights or obligations. This meaning is often found in historical contexts or in fixed terms such as 'Schuldbrief' (debt certificate).
Der König stellte dem Händler einen Schutzbrief für seine Reisen aus.
The king issued the merchant a letter of protection for his travels.
There are fixed verb combinations around 'Brief' (letter): you can 'schreiben' (write), 'bekommen' (receive), 'lesen' (read), 'öffnen' (open), 'verschicken' (send), or 'einwerfen' (drop into a mailbox) a letter.
Ich muss heute Abend noch einen wichtigen Brief schreiben.
I still have to write an important letter this evening.
When 'der Brief' (the letter/document) is mentioned in connection with a car, registration, or sale, it almost always means the vehicle registration document. It is the colloquial short form.
Ohne den Brief kannst du das Auto nicht verkaufen.
You can't sell the car without the vehicle registration document.
This meaning is usually found in historical or legal texts. Words like 'König' (king), 'Adel' (nobility), 'Urkunde' (certificate), or 'Schulden' (debts) in the sentence indicate that an official document is meant.
Im Mittelalter verlieh der Kaiser den Städten Freiheitsbriefe.
In the Middle Ages, the emperor granted cities charters of freedom.
to write
Schreiben refers here to the act of composing a text. Der Brief, on the other hand, is the written message that results and is usually sent by mail. When referring to the activity, use schreiben; when referring to the finished written document, use der Brief.

Der Brief an meine Tante liegt schon fertig auf dem Tisch.
The letter to my aunt is already finished and lying on the table.
Ich schreibe meiner Tante heute eine persönliche Nachricht auf Papier.
I’m writing my aunt a personal message on paper today.