Receiving a payment is acknowledging that a payment has been received from the client. When adding a payment, the funds will automatically be deducted from the client's outstanding totals.
Applying a payment allows you to keep track of payments against certain invoices. Applying a payment has no effect on the totals of a client's account, it only changes an invoice status from saying Unpaid to Paid.
Applying payments is the best way to run accurate accounting reports. The Invoice AR Aging, Payments Applied, Collections, and Invoice report all require payments to be applied to Invoices in order to show the proper totals. The totals from these reports are based on the invoice status.
For instructions on how to apply payments click here.