Ecclesiam nulla salus
Outside the Church there is no salvation
The use of this expression has a long history in the Church and has been used with various shades of meaning.
Augustine explicitly used the idea, however not so much as an exclusivist idea as an inclusivist idea. He also spoke of sheep without and wolves within. The venerable Bede discusses the Church as the Ark of Salvation, which like the Ark of old saved those within, while those without perished. The general tenor of the discussion by the fathers is largely an inclusivist idea, distinguishing the Church (as that was all there was for Christians to belong to) from those outside the Church.
In the West the idea developed a more exclusivist idea in the post schism period. This was allied with a developing understanding (in the West) that Church was defined by communion with the Ancient See of Rome. This may be allied to an overemphasis of the role of the Son in the Procession of the Holy Spirit (filioque).
The Eastern view clearly never embraced such an understanding of the Church, and remained/s solidly biblical in its understanding of the procession of the Holy Spirit and its rejection of the filioque. In Eastern theology there is an acceptance of the vastness of God's love, and whilst they are given to great precision in the finest theological points, the eternal state of a given human being is inefable (unable to be told). As such the East has retained a more inclusive understanding of the term.
Vatican II and the Post Vatican II Church has also gone about the work of understanding the term perhaps now to infer that anyone who is saved is ultimately a member in some sense of the Church. In the Spirit of Vatican II they are moving / have moved to a more inclusive understanding of the term.