It would be best to hear from someone from the RPSI to clarify, but I do live in Rheinland Pfalz not far from the border of Saarland, so I can at least say that the names Rheinland Pfalz and Saarland are the names of the German States where the breed registry originates.
Zweibruecken is the city (in Rheinland Pfalz) where the State Stud is. It was established by Herzog Christian IV. von Zweibrücken in 1755. As far as I know, this is why they horses are referred to as “Zweibrueckers” even though the registry name refers to the States.
Rheilanders are a different registry based near the border of Rheinland Pfalz and Nordrhein-Westfalen not far from Cologne in Moenchengladenbach.
It can definitely be confusing!