Pieds can have no ringer white, but there is a specific Pied pattern that makes a Pied a pied and not a ringer.
I don't have any photos at this time to show you the difference, but basically, a Ringer is an animal with a regular pattern but a white patch or splotch.
Pieds have a distinctive pattern that goes with the white that they have as well.
Hopefully someone else can share with you those distinctions, or you can check out this link. Jon does a good job of explaining it
http://www.nextworldexotics.com/hgpd.htm