Taiji, originated in China. There, long before inception of a formal ranking system such as "black belt" or "black sash" there were teachers of Chinese kung fu and "ranking" was recognized within relative place within the "family" or "clan." In this system, relative position within the family defined a practitioner's rank and status within the clan "family." Thus, adopting place within the family as a rank designator, the gao shou (expert) leading the instruction was the "shr-fu" (father-teacher; also written "sifu" and "shifu") Within this family-clan rank structure, members were (and still are, where used) designated as senior "old teacher" of the system shr-ye (grandfather teacher), kung fu "brothers" shr hsung-di and "uncles" as either shr-bao or shr-hsu (older or younger uncle in relation to the "shrfu"-or "father-teacher of the martial style).
A person who receives formal lineage becomes a "disciple" of the master, literally ru men di tse, or "one who is permitted through the 'inner door,'" through formal Confucian ceremony makes public oaths to assume more deep, personal responsibility to the master and art. After formal acceptance as a disciple, the new initiate begins to be introduced to closely held secrets of the art. By tradition, every true master has deeper knowledge of the art that are passed to only a few initiated disciples. Most intriguing is the transmission of lineage. Although the term is often misused and misrepresented, true lineage is passed to the student through formal Confucian ceremony. True lineage is transferred when there was no gap and documented lineage has passed through from generation to generation via induction during formal ceremony. Although there is no test for lineage, since it is generally thought of as representing access to special knowledge as well as responsibility to the art, over time--at least within many groups--the teacher is assumed to have been extremely careful when accepting a disciple.
It is also important to bring up the matter that some teachers prefer to neither use, nor issue no rank whatsoever. They practice and get better and for them this is enough. I hold the deepest appreciation for some of my teacher who, at least when I studied with him, was not concerned with formal ranking. In the end, if quality is important, that is what the aspiring student will be concerned with. Formal ranking and lineage may, or may not show up, but that doesn't really matter. What matters is the degree of depth and dedication to the art, and the joy this brings to embrace a rare and beautiful thing.