For the most part, there are four basic types of routers that you may encounter on a computer network.
The Edge Router
The edge router is, as you may have guessed, one that sits on the edge of an ISP's network. It is the edge router's job to route data externally to either another service provider or a large enterprise's autonomous system. These are most common in the world of business.
Subscriber Edge Router
The subscriber edge router is similar in function to standard edge router except in its function on the edge of the subscriber’s network and that it is used to transmit data into the subscribers network.
Inter-Provider Border Router
Figure provider border routers are used to interconnect ISPs. These routers maintain what is known as the BPG which allows two routers, such as an edge router and the subscriber edge router, to talk to each other and transmit data.
Core Router
A core router is used inside an ISP and transmits internally. They may be used to connect as your border routers or simply to pass signals within the network. While traditionally the core has been in the backbone of the system, as the design of modern networks changes, finding the core can be more and more challenging. Generally where the drivers are now is consider the core.