On the contrary, “subsists in” in Lumen gentium 8 and CCC 816 means the same thing as “is.”
If this were not the case, then Pope Pius XII would have been seriously mistaken when he rejected the following errors in section 27 of his 1950 encyclical Humani generis:
Not to put too fine a point on it, but i disagree with that conclusion as the original draft used the word “is” and the final draft promulgated contained the word subists.
John Paul explicitly talks about this in the book, Crossing the Threshhold of life. Obviously, this isn’t a magesterial text, however, it does indicate the pontiff’s understandinf og the word subsist.
In the chapter titled, “Is Only Rome Right?”, John Paul II speaks about salvation and its relation to the Church.
First JPII explains:
the
Christian doctrine of salvation and of the mediation of salvation, which always originates in God. “For there is one God. There is also one mediator between God and the human race, / Christ Jesus, himself human” (1 Tm 2:5). “There is no salvation through any other name” (Acts 4:12).”
He then affirms:
It is therefore a revealed truth that
there is salvation only and exclusively in Christ. The Church, inasmuch as it is the Body of Christ, is simply an instrument of this salvation.
John Paul II then explains what this means:
Man is saved in the Church by being brought into the Mystery of the Divine Trinity, into the mystery of the intimate life of God…
Thus, the Council is far from proclaiming any kind of
ecclesiocentrism. Its teaching is
Christocentric in all of its aspects, and therefore it is profoundly rooted in the Mystery of the Trinity.
JPII also affirms the council teaching of Vatican 2 affirming the necessity of the Church:
men cannot be saved who do not want to enter or remain in the Church, knowing that the Catholic Church was founded by God through Christ as a necessity"
(Lumen Gentium 14).”
Then JPII goes on to explain exactly what Lumen Gentium is talking about in regards to their relation to the Church.
People are saved
through the Church, they are saved
in the Church, but they always are saved by the grace of Christ. Besides formal membership in the Church,
the sphere of salvation can also include other forms of relation to the Church (emphasis mine). Paul VI expressed this same teaching in his first encyclical,
Ecclesiam Suam, when he spoke of the various
circles of the dialogue of salvation (cf.
Ecclesiam Suam 101-117), which are the same as those indicated by the Council as the spheres of membership in and of relation to the Church. This is the authentic meaning of the well-known statement “Outside the Church there is no salvation.”
He also goes on to say:
It would be difficult to deny that this doctrine is extremely
open. It cannot be accused of an
ecclesiological exclusivism. Those who rebel against claims allegedly made by the Catholic Church probably do not have an adequate understanding of this teaching.
JPII then explains the authentic meaning of the word subsist in as opposed to “is”:
Although the Catholic Church knows that it has received
the fullness of the means of salvation, it rejoices when other Christian communities join her in preaching the Gospel.
This is the proper context for understanding the Council’s teaching that the Church of Christ "subsists" in the Catholic Church (cf. Lumen Gentium 8; Unitatis Redintegratio 4).