"Routing is the process of deciding where to send a received packet. If this is the destination host we send it up the stack to an application process. If not we use the destination IP address and the IP routing table to choose an interface that is the best route to the next hop.

In that context forwarding is the act of sending the packet to the next hop. It also has a more generic meaning of passing on something received from the network rather than accepting it on this host; which can also be applied to application level traffic like e-mail and newsgroup messages - often in the expression “store-and-forward”."