Asian martial arts traditionally use terms that are usually translated as "teacher"and the use of "master" was a Western invention derived from 1950s United States war veterans returning home with stories of the incredible martial feats of certain individuals and groups. Subsequently, they found their way into martial arts culture as marketing tactics to the extent that the titles are aligned to the 'elderly martial arts master' stock character. In Asian countries, such titles are more commonly reserved for religious leaders and saints.
The use of "master," "grandmaster," etc. is decided within an individual art or organization. The use may be self assigned; for example having promoted a student to 'teacher' level, or may be assigned by a governing body in arts with a more formalised structure, and some do not use it at all, for historic reasons or to avoid the 'elderly master' stereotype. The modern use of Dan rankings and Black belt and Red belt in martial arts both derive from Judo where they were adopted by its founder Kanō Jigorō.