Payment bonds are a type of contract bond that assures completion of the obligee´s requirements in a satisfactory manner. This bond guarantees all participants (suppliers, subcontractors, and laborers) will be paid should the contractor default.
A performance bond guarantees satisfactory performance of all duties specified in the contract. Examples would the labor of all sub-contractors, suppliers, and payment of materials. The principal will require the performance bond once awarded the contract.
So in short, the difference is payment bonds cover payment of materials and workers, and performance bonds make sure the work is done to specification and per the terms of the contract.