The two words are used as though they mean the same thing, and quotations are compared as though they cover the same work. They do not. Forwarding is a part of the shipping process — the movement of goods from one place to another. Freight forwarding is the management of the entire shipment, origin to destination.
The difference shows up when something goes wrong. A price that only covers the truck is cheaper than a price that covers the truck, the paperwork, the clearance, the storage and whoever has to answer the phone at 2am.