Generate a proof of your incoming/outgoing payment by supplying the transaction ID, the recipient address and an optional message. For the case of outgoing payments, you can get a 'Spend Proof' that proves the authorship of a transaction. In this case, you don't need to specify the recipient address.
Verify that funds were paid to an address by supplying the transaction ID, the recipient address, the message used for signing and the signature. For the case with Spend Proof, you don't need to specify the recipient address.