Hi BarbaraTherese,
I am a full pledged and vowed member of the Confraternity of Penitents. PM me if you have questions.
Both the Confraternity and the BSP live the original 1221 Rule of the the Franciscan Lay Order, adapted to contemporary life. There may be small differences (I haven’t looked). For example, someone mentioned to me that the BSP mitigates the dress code for Sundays and solemnities, while we do not.
The Confraternity is constituted under the vigilance of the Diocese of Providence. I do not know the precise jurisdiction of the BSP, but they are centered in Minnesota. It is my understanding that they ARE properly constituted according to canon law, just as we are.
So, I can tell you about the CFP, but I can’t really give you details about the BSP.