die Bestellung
order
A request to a company to deliver certain goods or provide a service, usually in exchange for payment.
Ich habe online eine Bestellung für neue Bücher aufgegeben.
I placed an order online for new books.

order / reservation
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order
A request to a company to deliver certain goods or provide a service, usually in exchange for payment.
Ich habe online eine Bestellung für neue Bücher aufgegeben.
I placed an order online for new books.

'Die Bestellung' (the order/reservation) is the noun related to the verb 'bestellen' (to order/reserve). The ending '-ung' turns the action into a feminine noun that refers to the order or the process itself.
Die Bestätigung Ihrer Bestellung erhalten Sie per E-Mail.
You will receive confirmation of your order by email.
The many meanings can be distinguished well by context: If it is about goods, it is a purchase order. If it is about a restaurant, it is a reservation. If it is about fields, it is agriculture. If it is about an office, it is an appointment.
Meine Bestellung von Kleidung ist noch nicht angekommen.
My order of clothing has not arrived yet.
In connection with buying goods, the verbs 'aufgeben' (to place, as in placing an order), 'stornieren' (to cancel), or 'erhalten' (to receive) are often used.
Ich möchte meine Bestellung bitte stornieren.
I would like to cancel my order, please.
When you call a restaurant or hotel to reserve a table or a room, you can use 'Bestellung' (reservation). A typical question is: 'Haben Sie eine Bestellung auf den Namen Meier?' (Do you have a reservation under the name Meier?)
Guten Abend, ich habe eine Bestellung für zwei Personen für 19 Uhr.
Good evening, I have a reservation for two people for 7 p.m.
This meaning is very specific and is used almost only in agriculture. It describes work in the field, especially sowing.
Die Bestellung des Ackers muss vor dem ersten Frost abgeschlossen sein.
The cultivation of the field must be completed before the first frost.
Appointment to an office is referred to as 'Bestellung' (appointment). This usage is limited to formal, official, and legal contexts.
Die Bestellung zum Geschäftsführer erfolgt durch den Aufsichtsrat.
The appointment as managing director is carried out by the supervisory board.
assignment / order / mission
'der Auftrag' and 'die Bestellung' can both mean in business that someone wants to get something in exchange for payment. 'Bestellung' is used especially when you request goods or a service from a company, for example online, in a restaurant, or from a supplier. 'Auftrag' sounds broader and often more businesslike: it can also mean a larger piece of work or a project that someone is supposed to carry out. Learners may confuse the words because a 'Bestellung' can be a kind of 'Auftrag'. For a package, you usually say 'Bestellung'; for a larger work assignment, 'Auftrag' is more likely.

Meine Bestellung ist heute Morgen mit der Post angekommen.
My order arrived by mail this morning.
Die Kundin gibt der Druckerei den Auftrag für neue Flyer.
The customer gives the print shop the assignment for new flyers.