"What are core routing and edge routing capabilities?"
"Routing" not routers? With regard to "routing", very much the same capabilities, regardless of where in the network routing is being done. I.e. ingress packets arrives, examine destination address, route it, if possible, if not, drop packet.
However, the capabilities of routers, used in different roles, may differ, sometimes much, physically or logically.
For example, as "core" routers are in/at the core of the network, they often have routing (volume) capacity beyond "edge" routers.
Or, for example, as "edge" routers are at the edge of the network, they might go beyond just routing, by doing deep packet analysis to determine if packets entering the network conform with network usage policies.
