Open any booking in the diary - booked, finished or a no-show - and press Invoice. FullDiary makes a draft invoice for the same customer, with the service and its date on the line at the full price. A deposit the customer has already paid shows as a negative line, so the total is what is still owed. Your payment terms and standing notes go on as they do on any invoice.
It opens in the editor, so you can check it, change a line and send it. Pressing Invoice on the same booking again opens the invoice you already made, and if you delete that invoice the booking can be invoiced again. It counts as one of your invoices for the month: 3 a month on Free, unlimited on Pro.
If you sold products or a pass with the booking, Make an invoice on the Sell sheet makes a draft for the whole sale with the payment shown, so it reads as paid. The same sheet has Email a receipt for a customer who only wants proof of payment.