Process ids can be different on OSPF routers. The process id only refers to OSPF process running on that particular router. You can run muliple OSPF processes on a single router but that might consume your CPU/Memory a lot.
When configuring OSPF on a Cisco router, the process ID is simply a way to identify a routing process. It has nothing to do with the autonomous system like EIGRP, IGRP or BGP. I'm more inclined to say that this is a "fancy" way of identify two separate routing instances on a router. Further more, having different process id means that you can do stuff like "show ip ospf " to find out exactly what each OSPF routing process do for you.
when you use mpls/vpns and you want use ospf between the customers network and the provider you use different ospf process ids which gives you in addition with a vpn name a clear separation between the customers.
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...