Types of letters

Order. Covering letter
1. Opening:
Please find enclosed our order № 4378 for (items, materials, services, etc.).
2. Payment: confirm the terms of payment:
We would like to confirm that payment is to be made…
3. Discounts: confirm the agreed discounts:
Finally, we would like to say that the 25% trade discount is quite satisfactory.
4. Delivery and methods of delivery.
5. Packing: advise your supplier how you want your goods will be packed.
6. Closing.

Order form - a document showing the number and type of products that you want when you order goods:
(https://dictionary.cambridge.org/ru/словарь/английский/order-form)
See examples at http://templatelab.com/purchase-order-templates/#Purchase_Order_Templates

Other specimens
*Order acknowledging letter (short):
Thank you for…
Your order №… is now being processed.
We are now dealing with it and you may expect delivery within the next 3 weeks.
We are pleased to say that we have already made up your order №… for 50…, and we are now making arrangements for shipment to Rotterdam.