Routing is the act by which a host receiving an IP packet to be sent to another destination, makes the decision of where to next send that packet, based on its knowledge of the network. Routing happens at level 2, that is, at the IP level.
A router is an equipment capable of:
Note: ANY host can be a router, provided that the above two conditions are met. Therefore, a host can make a routing decision to send a packet, without being a router, since that host will have only one interface and will not forward packets.
In the case of a non-forwarding host equipped with 2 or more interfaces, the term multi-homed host is used.
Routers are also called gateways.