On this point, Koshinto is very similar to late Edo-period Shinto sects, notably the Kurozumikyo sect, and indeed, quite a few people choose to describe Sect Shinto's religious organizations as Koshinto.
この点は黒住教をはじめとする幕末期以降の教派神道と共通しており、事実、教派神道系の教団には古神道を名乗るものが少なくない。