The "Balance list by invoice date" lists all positions of a specific customer which were billed in the chosen period. They are grouped by reg with a balance amount per reg and a total one.
The "Reservation balance list by arrival date" looks similar, but the date selection is on the arrival date of the reservation. Then we take all billed invoices which belong to those reservations.
The lists can be accessed via the guest/customer database tab “Prices”: