The expression “Conciliar church” obviously expresses a reality, something real, namely the mass of people and institutions professing themselves to be Catholic but in fact sliding into the practice of the new humanist religion of the Second Vatican Council. “Sliding,” because Conciliarism, or neo-modernism, is precisely designed to enable Catholics to maintain the appearances of the Faith while they empty out the substance. Catholics in the concrete can make this process as fast or as slow as they wish, they need not even take it all the way to its conclusion, but Conciliarism in the abstract is utterly opposed to Catholicism and, taken to its conclusion, it destroys both Faith and Church, as it was meant to do.
The process is not difficult to observe or to understand, but liberals at the head of the Society of St Pius X, seeking reconciliation with the Conciliarists in Rome, have done their best to confuse the question of the Conciliar church and the Catholic Church. For instance the Catholic Church is visible, they will say, and the Conciliar church is the visible church, so the Conciliar church is the Catholic Church, an argument dismissed years ago by Archbishop Lefebvre as “childish” (many churches are visible that are not Catholic). Equally childish is the argument that there is only one Church, so the Conciliar church and the Catholic Church must be one and the same (there are thousands of false churches).
The truth is not too complicated. The Catholic Church is a living organism, both divine and human, like its Founder, Jesus Christ. As divine, as being his Immaculate Bride, it cannot be corrupt or corrupted, but as being made up of sinful human beings, it can partially rot just like any other living organism. So one useful way to understand how the Conciliar church relates to the Catholic Church is to think of a rotten apple.
On the one hand the rot belongs to the apple. All rot was once apple. The rot is a corruption of the apple, a parasite on the apple, it could not exist without the apple and it remains firmly attached to the apple unless and until the rotten part falls off. Likewise Conciliarism belongs to the Catholic Church insofar as everything Conciliar was once Catholic, it is a corruption of the Catholic Church, a parasite on the Catholic Church, it could not exist without the Catholic Church, and it remains firmly attached to some part of the Catholic Church unless and until it destroys that part, as it was designed to do.
On the other hand the rot does not belong to the apple. No apple was ever meant to go rotten. All rot is a transformation of some apple, a corruption and parasite of apple, transforming it for the worse, resulting in something quite different from apple, something which nobody in his right mind would dream of eating or of saying that it was no different from apple. Likewise Conciliarism does not belong to the Catholic Church, it is a corruption of something Catholic and is a parasite on whatever is Catholic. It transforms (a human part of) the Catholic Church for the worse, resulting in something essentially non-Catholic which no Catholic in his right mind would call Catholic or want to associate with, on pain of losing his faith.
In brief, Conciliarism is rot, and the “Conciliar church” is the one divine-human Church being rotted in one or other of its human aspects. Of course the Catholic Church will last to the end of the world (Mt. XXVIII, 20), while the “Conciliar church” is merely one in a long line of parasite churches down the ages, living on what they rot and rotting what they live on. A plague on all liberals, confused and confusing!