The carrier is the company that undertakes, under a contract of carriage, to transport goods to their destination and deliver them there. In German law the term is defined in Section 407 of the Commercial Code (HGB).
Distinction: the carrier performs the transport itself (or via subcontractors); the forwarder organises it.
Duties: taking over, carrying and delivering the goods; liability for loss and damage (under CMR in international transport).
Economics: the carrier bears the cost of the trip – so it needs to know before accepting whether the freight rate covers it.