It's not just that. This was quarter a century ago in a country that no longer exists so things may be different where you live now but... ...once upon a time, an invoice was a tax document. In a sense that as far as the taxman was concerned, the date on your invoice was the date when the income or expenditure (depending on whether you are the seller or buyer) was counted from. Of course, this is not necessarily convenient, especially if you have customers who delay the payment: you start paying tax on the money you have not received yet. So companies started sending you invoices after you paid for the goods.
For customers with accounting department demanding invoices to authorize payment, an entity called "pro-forma invoice" was invented. This document was not an official tax document and could be discarded once the real invoice arrived. Of course, in these enligtened times, we do not resort to such practices