Taoism's priesthood is not a single undifferentiated office, and the Celestial Master's position within it is best understood by contrast with the much more general term daoshi, which simply denotes any ordained Taoist priest regardless of rank, lineage or specific school. A daoshi may serve a local temple, perform household ritual, conduct funerary rites or hold any of a wide range of ordinary priestly functions across Taoism's many distinct lineages and schools, of which the Way of the Celestial Masters is only one, if a particularly old and influential one; there is no single daoshi hierarchy uniting all of Taoist practice under one central authority the way, for comparison, the Catholic episcopate is unified under Rome.
The Celestial Master title sits apart from that general priestly vocabulary specifically because it names one singular office, the hereditary head of one specific lineage's movement, rather than a rank any qualified priest within Taoism broadly might eventually reach. A daoshi ordained within the Celestial Masters' own tradition answers, at least nominally, to the Celestial Master's authority; a daoshi ordained within a wholly separate Taoist lineage, of which historically China has had several significant ones, does not, and has no equivalent singular hereditary head of their own tradition to answer to at all. The distinction matters for understanding Taoism's institutional structure honestly: it has never been organized as a single unified church with one leader, and the Celestial Master's long, singular hereditary lineage is a genuinely unusual feature within Taoism's broader, more institutionally fragmented landscape rather than representative of how Taoist authority typically works.