Here are some texts on membership, a concept used to identify the Body of Christ, which is the Catholic Church (a visible society.)
[quote=Pius XII, Mystici Corporis]22. Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. “For in one spirit” says the Apostle, “were we all baptized into one Body, whether Jews or Gentiles, whether bond or free.” As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith. And therefore, if a man refuse to hear the Church, let him be considered - so the Lord commands - as a heathen and a publican.  It follows that those who are divided in faith or government cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit.
Lumen Gentium, which spent a lot of time discussing other relationships, like partial communion, that separated Christians could have with the Church, distinguishes them from those who are united as members of the Body. As Cardinal Ratzinger noted in my previous post, it spoke of degrees of communion, with “full incorporation” being used as the equivalent of membership.
[quote=Vatican II, Lumen Gentium]They are fully incorporated in the society of the Church who, possessing the Spirit of Christ accept her entire system and all the means of salvation given to her, and are united with her as part of her visible bodily structure and through her with Christ, who rules her through the Supreme Pontiff and the bishops. The bonds which bind men to the Church in a visible way are profession of faith, the sacraments, and ecclesiastical government and communion. He is not saved, however, who, though part of the body of the Church, does not persevere in charity. He remains indeed in the bosom of the Church, but, as it were, only in a “bodily” manner and not “in his heart.”(12*)
The Decree on Ecumenism makes the same distinction between full incorporation/membership and other modes of communion and partial incorporation and belonging, noting that those baptized, but lacking certain elements, need to be fully incorporated:
[quote=Vatican II, Unitatis Redintegratio]It was to the apostolic college alone, of which Peter is the head, that we believe that our Lord entrusted all the blessings of the New Covenant, in order to establish on earth the one Body of Christ into which all those should be fully incorporated who belong in any way to the People of God.
The same decree notes that the separated brethren “are not blessed with that unity” that we believe “subsists in the Catholic Church as something she can never lose.”
Again this distinction is made in the Catechism in paragraphs 836-838. After quoting the passage from Lumen Gentium I quoted above, the CCC mentions those who lack some of the elements of membership described by Pius XII and Lumen Gentium (ie they do not profess the Catholic faith or have not preserved hierarchical communion under Peter)–they are instead in an imperfect communion:
[quote=CCC]838 "The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter."322 Those "who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church."323 With the Orthodox Churches, this communion is so profound "that it lacks little to attain the fullness that would permit a common celebration of the Lord’s Eucharist."324