There are certain labels people use to brand things they talk about frequently. Often these are a mere convenience, but often they indicate the understanding (or misunderstanding) that exists in the mind of the label-user about the reality he is labeling. If you use the label “the guy with the big nose” with an audience that grasps the relative nasal proportions of all the people you could possibly mean, then the label has some effectiveness (if not politeness), and fits into that category of “convenience.” If you call that man, on the other hand, a “sub-human,” because you operate under the delusion that people with such prodigious proboscises belong to a lesser species, then your label reflects an anthropological misunderstanding of the person about whom you speak.
Some Catholic traditionalists refer to the “Conciliar Church.” What exactly they mean by this will vary depending on whether the label-user is a sedevacantist, an SSPX supporter, etc. For the sedevacantist, it represents a false “church” full stop, complete with a false pope, false bishops, etc. It simply isn’t the Catholic Church at all, but an alien sect. For others, the term is a way to label those in the hierarchy who represent a certain regime of novelty, but they actually do hold legitimate office in the Church. The term “Novus Ordo Church” has a similar usage.
I’ve heard both these terms bantered about for years, and have come to the conclusion that they are very dangerous labels that betray — or at least can betray — a flawed notion of what the Church is. And this removes the label from the “convenient” category to the “misunderstanding” category. As soon as you put the noun “Church” after the predicate “Conciliar” or “Novus Ordo,” the implicit conclusion is that this “Church” (or “church”) is something other than the Catholic Church. Whoever accuses the legitimate Holy Father of leading the “Conciliar Church,” has it that he heads an alien sect, not the Catholic Church. (Bishop Williamson’s contention that the Pope is at the same time head of both — a false sect and the true Church — is a piece of psychedelic theology that only emboldens the sedevacantsists to point and laugh, while giving mainstream critics of the SSPX more ammo to fling at them.)
The net result is this: If you refer to the “Conciliar Church” or the “Novus Ordo” Church and you mean by that an institution headed by Pope Benedict XVI, but not the Catholic Church, then you are a schismatic. And schismatics — need I say it? — go to hell.