Internal Router :All interfaces of the router are in single area. It does not mean that area has to be Area 0
Backbone Router: At least 1 interface in area 0.A router can be both an Internal and Backbone router if all its interfaces are in Area 0.
Area Border Router: has interfaces in multiple areas.at least one interface in Area 0 and another interface in a non-backbone area. ABRs are also one of two router types that can perform OSPF route summarization.
Autonomous System Border Router: Act as gateways between OSPF and other routing protocols. It is performing route redistribution by injecting routes from another source into the OSPF domain.