In Catholic circles anyway, these terms may still be evolving, for while some define a Traditionalist as a member of a [size=2]schismati[/size]c group, there are many Catholics who call themselves Traditional Catholics or Traditionalists yet claim union with the Pope, the Bishop of Rome. Such Catholics do not deny that Vatican II was a legitimate council yet they have a preference for the approved Tridentine Mass and may often, or always, attend one. They may have some concerns as to how Vatican II has been implemented, but they do not question the legitimacy of the Roman Missal promulgated by Pope Paul IV in 1970, which is often called the New Order of the Mass or the Mass in the vernacular, as Schismatics do. They just don’t like it, and prefer the Tridentine Mass, or Latin Mass.
It seems helpful, therefore, to differentiate between those who consider themselves Traditional Catholics in communion with Rome, and those who do not. Perhaps “Radical Traditionalists” or “Schismatics” would be a better term for such Catholics. Those who belong to the Society of St. Pius X (SSPX) question the legitimacy of the Roman Missal promulgated by Pope Paul IV in 1970; Sedevacantists reject all the popes since Pope Pius XII, thus rejecting all the “Vatican II popes”, they believe that these men are heretics due to many of the Vatican II decrees and subsequent papal promulgations and a small group has elected popes of their own.