Actually, I think ringers arent piebalds at all, but they are actually frequently confused with piebalds. They share no similar genetics, and the ringer gene is still a mystery, I believe.
Heres two pictures of ringers:
The body patterns on these ringers are normal. The odd white spots are random and are often the reason people confused them for piebalds. You can tell they arent piebalds because pieds have a very aberrant and wild body pattern, and those ringers look nothing like it.
Heres a picture of a low white pied: