Should a receipt be issued for pre payment online rather than an invoice?

Following on from our query regarding invoices being created when a patient pre-pays, would it be more accurate to issue a payment receipt and the payment amount would show as a credit on the account. Then we could invoice the patient after the appointment has actually taken place. this would mean that all the accounting would be more accurate and would eliminate problems caused by patients cancelling or changing practitioner etc. Is it possible to separate the receipts and invoices in this way?