This is the same thing. A final invoice with an invoice number, date of the bill/invoice. Once created, the only changes that can be made is to apply payments to the bill.

Guest Bills Contain the following information:

A reservation confirmation is emailed to the guest when they make a booking on the booking engine, or if you choose to email a confirmation of the reservation from within the diary. It shows the current state of a reservation. It changes if the reservation is updated, e.g. rooms added or cancelled or dates changed.

Contains the following information

A VAT breakdown is not shown on the booking confirmation.
"Revenue" is not included in financial reports when a booking is made.

This is a copy of a bill before it is generated. It can be used on the day of checkout for the guest to peruse prior to checking out to resolve any issues before the final guest bill being generated.

The pro forma shows all the information in the Guest Bill/Invoice except there is no invoice number, the pro-forma does not alter any figures in the financial reports.

If the guest is looking for a receipt of payment, you can either send them the Reservation confirmation, as it will show applied payments or if a bill has been created for the reservations the Guest Bill can be supplied to them as it will also show any payments applied to the bill.