The Approved Column shows the number of approved transactions.  This is the number your commission is paid from.  This number may differ from the qualified column for a variety of reason.  The Qualified column is a reporting of a technical transaction. Basically, a qualified transaction mean the tracking URL set the cookie and the confirmation pixel found the cookie and reported back successfully. 

Business Logic:

If you have 100 qualified transaction and three of these transactions contained fraudulent information, your affiliate manager will unapproved three transactions.  Reporting will then display 100 Qualified and 97 Approved transactions.  If you have any further questions on number discrepancies, please contact your affiliate manager.