Dalai Lama and Panchen Lama are two great disciples of the leader Tsongkhapa of Gelug Sect. After years, there are two different kinds of inheritance system developed related with them.
As for the politics, Dalai Lama gets much more power than Panchen Lama. Because Dalai Lama ruled the Shannan Prefecture which the capital of Lhasa is almost considered as the central government of Tibet.
The name of Dalai Lama has been confirmed during the reign of the 3rd Dalai Lama Sonam Cyatso since 1578. Sonam Cyatso persuaded Altan Khan who was the leader of Tumo Tebu tribe to believe in Buddhism Sect, when he propagandized Buddhism in Qinghai region. After that, Sonam Cyatso and Altan Khan conferred each other in politics. The name of Sonam Cyatso given by Altan Khan is "Sheng Shi Waqir Dalai Lama". The words of "Sheng" "Shi" and "Waqir" meant the superior man with abundant knowledge in Exoteric Buddhism (including Mahayana and Hinayana) . The word of "Dalai" means the ocean in Tibetan language and the word of "Lama" means the great master in Tibetan language.
Then, Sonam Cyatso asked for conferring by Ming Dynasty. Since 1587, the 3rd Dalai Lama has been conferred officially to public by Ming Dynasty. The 1st Dalai Lama and the 2nd Dalai Lama have been subsequently confirmed by generations. They are respectively Gendun Tsuba and Gendun Gyatso.
During the reign of Shunzhi Emperor of Qing Dynasty (in the year of 1653), the 5th Dalai Lama has been invited to come to Beijing and conferred officially the Dalai Lama, besides the golden seal and golden book. Since then on, the name of "Dalai Lama" has been got much power of politics and law.
Due to govern Tibet region well, the 7th Dalai Lama has been ordered to manage the local affairs, which is considered as the beginning of the combination of politics and religion.