This is usually due to "on-hold" claims. "On hold" claims are partially paid, meaning only the procedure or the surcharges have been paid. This is why they are not showing up in the “Paid” section of the Billing Overview.
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When the "on-hold" claims are fully paid and released from MSP they will move over to the “Paid” section of the Billing Overview. That’s why it looks like the total MSP “Paid” amount is higher, because it includes the partially paid claims, while Dr. Bill’s numbers are lower because we do not consider the "on-hold" claims paid yet.  
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Once the "on-hold" claims are completely paid, they will show on the Billing overview and match MSP’s total paid.