Is it true that when Muhammad died, a group o Muslims leaders chose his successor, called a caliph

Yes, it is true. This started a long tradition of passing on the role of Muslim leader. The Caliph are referred to as, "Successor of The Messenger of God." During the selection process the masses are not allowed to participate in the process since they may try to elect relatives to high positions of status. Only Muslims with official ranks are qualified for the selection process.