The Second Vatican Council used the philosophical term “subsists in” to clarify the ontological relationship of the “Church of Christ” to the “Catholic Church.”
Clearly, in the order of ontology, the Catholic Church is a broader entity, because the Church of Christ subsists in the Catholic Church, not the other way around.
As such, the Catholic Church can exist without the Church of Christ, but the Church of Christ cannot exist without the Catholic Church.
This is academic and Matthew summed it up concisely: “Thou art Peter and upon this rock I will build My Church [not churches] and the Gates of Hell shall not prevail” (Matt.
They cannot prevail because of sanctifying grace – whose source is the Catholic Church and whose fullness (along with the fullness of truth) is hers exclusively.
But because there are elements of grace outside the Catholic Church (Christian baptism, for example), the source of grace (in the order of grace) combined with sacraments as administered by the Catholic Church would make (in the order of society) the Church of Christ (in the orders of grace and society) a broader entity.
There is no contradiction here, and so it is proper to say there are two distinct designations here, but they comprise one complex reality.
Lumen gentium is precise: This one complex reality “is comprised of a divine and human element,” and can be “compared, not without significance, to the mystery of the Incarnate Word.”
As such, the Church of Christ and the Catholic Church can be compared to the two natures in Christ and why the Catholic Church can no more be considered human than the Second Person of the Blessed Trinity can be spoken of as a human person.
The Catholic Church is divine as the Second Person is divine and has two natures: the Church of Christ, which is human and the Mystical Body of Christ, which is divine.
This is why Pope Pius XII said the “Mystical Body of Christ” is the “Catholic Church” and the Council said: The “Church of Christ subsists in the Catholic Church.”
Lumen gentium explains this unambiguously in 8a and 8b (Flannery’s edition), but both paragraphs must be read as a unit, if murkiness is to be avoided. Paragraph 8a sums up the
Church’s teachings in five crisp sentences. We have presented them (in the interest of better understanding) in five one-sentence paragraphs as the whole paper is composed of one-sentence paragraphs:
“The one mediator, Christ, established and ever sustains His holy Church, the community of faith, hope, and charity, as a visible organization through which He communicates truth and grace to all men.
“But the society structured with hierarchical organs and the Mystical Body of Christ, the visible society and spiritual community, the earthly Church and the Church endowed with heavenly riches, are not to be thought of as two realities.
“On the contrary, they form one complex reality which comes together from a human and a divine element.
“For this reason, the Church is compared, not without significance, to the mystery of the Incarnate Word.
“As the assumed nature, inseparably united to Him, serves the divine Word as a living organ of salvation, so, in a somewhat similar way, does the social structure of the Church serve the Spirit of Christ who vivifies it, in building up of the body (cf. Eph. 4:15).”
Clearly then, the progressivists who posit the erroneous theory that “the Church of Christ is not the Catholic Church” are wrong. For Holy Mother Church has expressed (and teaches) the Church of Christ and the Catholic Church comprise one complex reality.