Carrier is a shipping line.
Forwarder is a service company, they are not a shipping line.
Basically, when you want to book empty spaces of a vessel. There are two options: 1st option is you can book them with a shipping line directly, they will issue MASTER BILL for shipper. 2nd option is you can book them through as forwarder, freight is often more expensive than booking with a shipping line directly, but they do extra services (local logistics), in this case, the shipping line will issue MASTER BILL for a forwarder, then forwarder will issue HOUSE BILL for shipper.
Sometimes forwarders books many empty spaces of shipping line, so they can get good freights, and in that case, if you book through forwarders, you will get more benefits: good freight, extra services.