The below scenario shows the different flavours of OSPF between CE-PE.
OSPF with unique process = O IA (OSPF Route)
OSPF with different process = O E2 (OSPF Route)
OSPF with unique Process ID but different domain ID = O E2 (OSPF Route)
OSPF with different process ID but unique domain ID = O IA (OSPF Route)
Below link is the complete document for same.
MPLS Traffic engineering VPN with OSPF Process ID vs Domain ID
Chetan Kumar Ress