The pre-1907 polity: the head of state
Bhutan was a well-established polity since its founding in c. 1626 by the Zhabs-drung Ngag-dbang rNam-rgyal, (the "Founder") a head of the 'Brug-pa monastic order immigrating from Tibet.
The Founder was the head of state; he went into "retreat" in 1651 and probably died shortly thereafter, but officially his retreat continued, and the polity was governed in his name, until the official disclosure of his death in 1705.
The Founder and his successors as heads of state had not an official style in that capacity. His substantive successors were his incarnations, who used the monastic title Zhabs-drung; the term Zhabs-drung Rin-po-che (The Zhabs-drung Enthroned) came into common use to refer to these successors; in communications with foreigners they were referred to as Dharmarājā.
After a dispute about the identity of the "true" incarnation of the Founder, the theory developed, and was codified in 1759, that the Founder had three simultaneous incarnations: Zhabs-drung sKu-sprul, Zhabs-drung gSung-sprul, Zhabs-drung Thugs-sprul, the "body", "speech", "mind" incarnation, respectively; and that it was the "mind" incarnation that was to rule the polity; the "speech" incarnation occasionally ruled during vacancies; the "body" incarnation was deemed to reside in Sikkim, and the line of this incarnation became extinct.
The term rGyal-tshab ("ruler's representative") was coined by chroniclers to denote the person who ruled in the name of the Founder "in retreat" (1651-1705); and used for the interim rulers after 1705 (some authors use it for ALL the successors, substantive and acting, of the Founder). The Founder's only son, 'Jam-dpal rDo-rje, had been intended to succeed him, but he predeceased him in 1648; the son's daughter was briefly installed as acting head of state in 1696.
The pre-1907 polity: the administration
The Founder delegated his monastic authority to a monk with the title rJe mKhan-po; his line of succession continues to the present day. For the day-to-day administration, the Founder appointed a deputy with the title 'Brug sDe-srid (in full: 'Brug sDe-srid Phyag-mdzod; transcription: Druk Desi; referred to by foreigners as Deb Rājā). This official and his 54 or 56 successors governed the polity in the name of the Zhabs-drung until the establishment of the hereditary monarchy in 1907, and appeared to foreigners to be the actual rulers. A list is provided by Aris (1979).