they're the same thing I believe, but barred is the coloration.
there's, buff, white, partridge, barred and silver penciled Plymouth rocks.:] (I'd live some silver penciled rocks but everyone's out or they're $15 per straight run chick. )
Yes, seconding what @nuthatched and @25chickens said, Plymouth Rock is a breed of chicken and Barred, White, Silver Penciled, (etc.) are varieties. Varieties are like sub-categories that are sorted by color. It took me forever to figure this out, chicken trivia is confusing!