To clarify:
The organization FSSPX (which predated Ecclesia Dei) being the Fraternal Society of Saint Pius the Tenth, or simply, “The Society”.
The Ecclesia Dei organization FSSP being the “Priestly Fraternity of Saint Peter”, or simply,”The Fraternity”.
And the Ecclesia Dei organization ICKSP being the Institute of Christ the King, Sovereign Pontiff”, or simply, “The Institute”.
Sorry, the P part of ICKSP is (Soon to be was? 🙁) “Priest” (not Pontiff...)