Forwarding consists of taking a packet, looking at its destination address, consulting a table, and sending the packet in a direction determined by that table.
Forwarding Table is also different from the Routing Table because the forwarding table is built from the routing table. The Forwarding Table contains the mapping from a network number to an outgoing interface (say eth0) and some MAC information, such as the ethernet address of the next hop. Think of forwarding as a link layer and below mechanism.
Routing is the process by which forwarding tables are built.
The Routing Table is the result of routing algorithms and generally only has network numbers and next hop information.