Noahide Judaism
Noahide Judaism is the Sabbath observant form of Noahism that distinguishes Hasidei Umot haOlam from Hokhmei Umot haOlam. A Noahide who believes in Noahide Judaism is called a Noahide Hebrew, a Ma'amin, a Toshav and a Ger Shaar or Ger HaShaar (proselyte of the gate). Unlike other kinds of Noahism, Jews believe that Noahide Judaism guarantees those who protect this covenant a place in the world to come.
Six of the seven laws are universal (don't steal, don't murder, don't be lewd, don't use G-d's Name in vain, don't idolize anything) but the 7th law is different for those who wish to follow Noahide Judaism. Whethe the 7th law concerns Deen or Animal dignity is worthy of discussion.
The 7th Law for the Ger HaShaar is based around keeping holy the Sabbath day which is the only one of the 10 commandments which specifically mentions the Ger Shaar. Nevertheless, a Noahide still may not observe Sabbaths in exactly the same way that Jews do. They have to have a slightly different way, and that is precisely what the Petter Chamor tradition is focussed on.
Most Noahide Hebrews tend to respect the Scribes and Pharisees more than most Jews do and are therefore often at odds with most Jews as a result.