Under the CMR, the carrier is the party that contracts the carriage, even if it subcontracts the haul. It answers for loss, damage and delay between taking over and delivery, subject to a limit of 8.33 SDR per kilo of gross weight (art. 23).
A forwarder who issues the consignment note in its own name acts as contractual carrier and takes on that liability towards the customer, even though the truck belongs to someone else. Worth knowing before you sign.