The Billed Hours and Billed Dollars will probably never match between these two reports because the information is gathered based on different parameters.  The Summary of Hours Report is showing you the Billed Hours and Billed Dollars values of the time WORKED during the report date range – regardless of when it was invoiced.  In other words, the values gathered for that information are based on the date of the fee transaction.  The Billing Realization Report is based on Invoice Date – what were the Billed Hours and Dollars on invoices generated during the report date range – regardless of the fee transaction date (when the time was worked).