Definitions of delivery receipt on the Web:

* Document a consignee or its agent dates and signs at delivery, stating the condition of the goods at delivery. The driver takes the signed delivery receipt to the service center for retention. The customer retains the remaining copy.
www.yrc.com/shippers/glossary.html

* A document used to obtain a signature from the consignee when a shipment is delivered. Upon signing one copy is given to the signor and one copy is obtained for our records. This document is also known as a “Proof of Delivery.”
oakhtraining.com/glossary_terms.htm

This is what the company receiving the goods issues to the company deliverying the goods. A GRV is normally printed on the "company stationery", and will have a sequential number.

The "Wareneingangsdatum" in your text would simply be "Date Goods Received"
The supplier of the goods will normally issue a Delivery Note (similarly, having a sequential number, and being of the commpany stationery of the supplier's company, sometimes called an "Lieferschein".
These terms would apply for domestic delivery, and my knowledge, are Biritsh in origin.
I believe the multiplicity of terms is due to two things:
1. air/road/sea freight - especially internationally. This has terminology of its own!
2. Many organisations have developed their own systems to deal with procurement and have (partially) adopted or adapted terms from freight organisations.
It is usually a good idea to look through your text to see what other parts of the procurement/goods received chain you are dealing with before choosing the term for just one item.

Laut Wilhelm Schaefers Wirtschaftswörterbuch Deutsch - Englisch

Inventory & Distribution – Incoming Receipt of Goods

In all instances I&D staff will coordinate the off-loading of the goods and sign the carrier waybill verifying the number of packages and the external condition of the goods received. The signed waybills and all additional paperwork will be forwarded with the goods when re-distributed to the end user department. Once received, the end user department is responsible to:
1.
Remove any paperwork from the shipping package and attach it to the packing slip.
2.
Verify the content of the packages to the packing slip and the purchase order and record any discrepancies or damage.
3.
Attach the packing slip and all supporting documentation (i.e., carrier waybill etc) to the receiving copy of the PO and date and sign for receipt of goods.