assignment / order / mission
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assignment
A specific task or work assignment that someone carries out for payment or on instruction.
Die Agentur erhielt den Auftrag, eine neue Werbekampagne zu entwickeln.
The agency received the assignment to develop a new advertising campaign.
order
An order for goods or services in a business context.
Wir haben einen großen Auftrag über 10.000 Schrauben erhalten.
We received a large order for 10,000 screws.
mission
An important, often moral or idealistic mission or purpose that someone sees for themselves or for a group.
Die Organisation sieht ihren Auftrag darin, den Regenwald zu schützen.
The organization sees its mission as protecting the rainforest.
The word derives from the verb 'auftragen' (to assign/instruct). When you 'jemandem etwas auftragen' (assign someone something), you give them a task. 'Der Auftrag' is therefore the task that you have been given.
Der Chef hat mir aufgetragen, den Bericht bis Freitag fertigzustellen.
The boss assigned me the task of finishing the report by Friday.
'Auftrag' (assignment/order) is often combined with fixed verbs that describe the life cycle of a task: you can 'bekommen' or 'erhalten' an Auftrag (get/receive an assignment), 'annehmen' or 'ablehnen' it (accept or reject it), 'ausführen' it (carry it out), and finally 'erledigen' it (complete it).
Die Firma hat den Auftrag für den Bau der neuen Brücke erhalten.
The company received the assignment to build the new bridge.
The expression 'im Auftrag von jemandem' (on behalf of someone) means that you do something for another person or company. It is often used in formal and business contexts.
Ich rufe im Auftrag von Frau Dr. Meier an, um den Termin zu verschieben.
I am calling on behalf of Dr. Meier to reschedule the appointment.
When 'Auftrag' (mission) describes an idealistic mission, it is often used with verbs such as 'sehen' (to see) or 'haben' (to have). The context is then not commercial, but moral or social.
Ärzte ohne Grenzen sehen ihren Auftrag darin, Menschen in Krisengebieten zu helfen.
Doctors Without Borders sees its mission as helping people in crisis areas.
job
Both Job and Auftrag can refer to a specific piece of work. Job is more colloquial and does not imply that the work was explicitly commissioned, whereas an Auftrag is normally assigned or given by someone. When referring to commissioned work, Auftrag is therefore the better fit.
Ich habe heute einen Auftrag von der Werkstatt zu erledigen.
I have an assignment from the workshop to complete today.
Ich habe heute einen Job in der Werkstatt zu erledigen.
I have a job to complete at the workshop today.
