The Invoice Report gives a general overview of each invoice either created or held. Should your app be deleted while you have held invoices, this report will still show active invoices so that you can reopen them on the app and hold them again. The report is designed to be like an Order History report, meaning if you click on the order, you can access its details.
For invoices, if you take a payment while the 'order' is still in invoice form, the Sales Summary will show it as a deposit. Once that invoice has been converted into an order and closed, that deposit is then recorded as an Applied Deposit.
Essentially, the Deposit Liability shows the amount of the sale that was made on an invoice, so it's tracked in the Liabilities section of Sales. Once that invoice is converted, the deposit is applied and tracked in the Payment portion of the Sales Summary as an Applied Deposit.