In the admin panel under Manage > Invoices, you will see a column for "Status". An invoice's status can offer helpful information about its creation and/or state:
Full Payment: The invoice has been paid in full.
Sent: The invoice has been emailed to the member with a link to log in and make payment.
Downloaded: An admin has downloaded the invoice as a PDF file.
Generated: The outstanding invoice has been generated for the member but not emailed to him/her.
Sending: The invoice is being sent to the member but may be in a queue of other emails.