Why does a Bill of Exchange serve as a matter of credit and payment at the same time?

You are in a subject where words have slippery meanings. "Credit" means to record a deposit of money, it also means a loan, and it has some other meanings. "Payment" might or might not mean that money has changed hands. "Bill" is a legally defined word, but it is often used to mean things that have nothing to do with the legal definition. For example, a paper dollar is neither a bill nor a note according to the legal definitions of those words.

As usual in politics, your question boils down to "What are you talking about?" and the only answer might be "What would you like it to be, and how many voters do you represent?"