If the Church of Christ "subsists in" the Catholic Church, yet "numerous elements of sanctification and of truth" are found, through the work of the Holy Spirit, in other Christian communities, are any of those communities properly called Churches? The Congregation for the Doctrine of the Faith (CDF) answers this in response to the fourth question in "Responses to Some Questions Regarding Certain Aspects of the Doctrine on the Church," a recent document clarifying certain elements of ecclesiology (the nature of the Church) explored by Vatican II.
The fourth question reads: "Why does the Second Vatican Council use the term 'Church' in reference to the oriental Churches separated from full communion with the Catholic Church?" The answer, the CDF explains, in found in another document from Vatican II, Unitatis Redintegratio ("The Restoration of Unity"): "Because these Churches, although separated, have true sacraments and above all--because of the apostolic succession--the priesthood and the Eucharist, by means of which they remain linked to us by very close bonds." In other words, they are properly called Churches because they meet the requirements in Catholic ecclesiology for being a Church. Apostolic succession guarantees the priesthood, and the priesthood guarantees the sacraments--most importantly, the Sacrament of Holy Communion, which is the visible symbol of the spiritual unity of Christians.
The Eastern Orthodox Churches, then, are "particular or local Churches," counterparts to the particular or local Churches that are in union with Rome. But because the Eastern Orthodox are not in full communion with the Catholic Church, "these venerable Christian communities lack something in their condition as particular churches."
Equally as important, the separation of the Eastern Orthodox Churches from the Catholic Church means that "the fullness of universality, which is proper to the Church governed by the Successor of Peter and the Bishops in communion with him, is not fully realised in history." Christ prayed that all would be one in Him, and, as Pope Benedict XVI clearly understands, that prayer compels him and his successors to work for the full, visible union of all Christians, starting with those who retain the status of "particular or local Churches."