Pius XII, in Mystici Corporis, teaches that the unique Church of Christ is(est)the Catholic Church. Lumen Gentium, on the other hand, changes the est to subsistit because it no longer identifies (est) the Church of Christ with the Catholic Church. This is to say that the Church founded by Christ exists in the Catholic Church, without excluding the other 'separated churches.' (The conciliar magisterium uses capital C for the 'separated Churches')
"In short, the Mystical Body of Christ has a greater extension than that of the Roman Catholic Church."
The error of Vatican II is that it reduces the Roman Catholic Church to a mere organization in which the Church of Christ subsists. It is a mere branch of the great trunk of the Church of Christ. But there are other branches.
This heresy reduces the body of the Catholic Church to a mere moral person, that is, an ecclesiastical corporation with a certain natural structure, governed by certain natural laws, with a certain natural unity. Unity of faith is reduced to an obedience to "church order," which is to say, an external observance of the faith rules of the day, by which the church is preserved in order. This reduces the notion of orthodoxy to a purely legal observance of the prevailing theology of the day.
Those familiar with modernism see its ugly face in this theory and practice. Pope Pius XII condemned this theory in his encyclical Mystici Corporis in 1943: