Peer
Peers are those gentles who are either "retired" royalty or members of one of the three Great Orders of the Society.
Royal Peers
Royal Peers are those who hold the rank of Viscount/ess, Count/ess or Duke/Duchess, indicating they have served as royalty and ruled either as Prince/ess of a principality or King/Queen of a kingdom.
Peers of the Society
These are gentles who are members of the Order of Chivalry, the Order of the Laurel and/or the Order of the Pelican. With the exception of Knights (part of the Order of Chivalry), who are addressed as "Sir", members of these orders are addressed as "Master" or "Mistress."