der Befehl
order / command
An instruction or order from a person with authority (e.g. in the military or the police) that must be obeyed.
Der General gab den Befehl zum sofortigen Rückzug.
The general gave the order for an immediate retreat.

order / command
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order / command
An instruction or order from a person with authority (e.g. in the military or the police) that must be obeyed.
Der General gab den Befehl zum sofortigen Rückzug.
The general gave the order for an immediate retreat.

The noun 'der Befehl' (order/command) is closely related to the verb 'befehlen' (to order/command). Someone who has authority can command something and thus gives a 'Befehl' (order/command).
Der Polizist befahl dem Fahrer, anzuhalten.
The police officer ordered the driver to stop.
To describe the content of an order, an infinitive construction with 'zu' is often used. The structure is: 'der Befehl, etwas zu tun' (the order to do something).
Die Soldaten erhielten den Befehl, die Stellung zu halten.
The soldiers received the order to hold the position.
In connection with authority, fixed verb-noun combinations are often used: 'einen Befehl geben/erteilen' (to give/issue an order), 'einen Befehl ausführen/befolgen' (to carry out/obey an order), or 'einen Befehl verweigern' (to refuse an order).
Der Kapitän erteilte den Befehl, die Segel zu setzen.
The captain gave the order to set the sails.
When it is about computers or technology, 'Befehl' (command) means an instruction to a machine. Typical verbs in this context are 'eingeben' (to enter), 'ausführen' (to execute), or 'speichern' (to save).
Der Computer hat den Befehl „kopieren“ nicht ausgeführt.
The computer did not execute the command 'copy'.
assignment / order / mission
'der Auftrag' and 'der Befehl' can both be an instruction to do something. However, 'Auftrag' sounds more like a task that someone is supposed to complete, often at work or for payment. The person usually has some responsibility for how they carry out the task. 'Befehl' is stronger and stricter. It comes from a person with authority and must be obeyed, for example in the military or the police. The words can be confused because both can come from above. In practice: an 'Auftrag' is supposed to be completed; a 'Befehl' must be obeyed.

Der Soldat führte den Befehl seines Offiziers sofort aus.
The soldier immediately carried out his officer's order.
Die Firma hat einen großen Auftrag für den Bau neuer Fenster angenommen.
The company accepted a large order to build new windows.