What would be the purpose of configurng an OSPF routing process on, say, a routed access layer switch, and giving it an OSPF process ID of 1, while creating an OSPF process on its OSPF neighbor and giving it a different process ID?
What is achieved by this? Two OSPF routers dont have to be using the same OSPF process ID to establish a neigborship and exchange routes, so what are the implications of using 2 different process IDs for adjacent OSPF routers?
No implications whatsover. The process ID is locally significant and allows you to have more than one OSPF process in a single OSPF capable device.