You will need to define custom Workflow notifications to achieve this functionality. You can have different templates to send to the Vendor and to the PR raiser. You can also achieve the mail to the vendor to be from the email id of the Buyer (PO creator).
Go to SPRO->SAP Netweaver -> Application Server -> SAP Business Workflows -> Notifications and configure the workflow.
We've had most of this functionality configured and implemented albeit in SAP SRM.