Some time ago, Pastor Wes White wrote a series of blog posts on the errors of the Federal Vision. In part 5 of the series, he addressed the traditional Reformed understanding of the Visible/ Invisible Church distinction and the Federal Vision's denial of it. As he has said,
Many Protestants today do not understand the importance of the visible/invisible Church distinction. However, for classical Protestantism, this distinction was a vital one with profound implications for the salvation of sinners and the life of the Church.
Classic Protestant theology defined the Church as true believers in Christ. Thus, Martin Luther said, “He who does not truly believe . . . does not belong to the Christian Church” (note how Luther uses the phrase “the” Christian Church” differently than the FV). Consequently, he adds, “If the Pope were not pious and holy, he could not be a member, much less the head of the holy Church.” Calvin speaks similarly, “To God alone must be left the knowledge of His Church, of which His secret election forms the foundation.” 4 Similarly, Charles Hodge stated, “If a man is not justified, sanctified, and consecrated to God, he is not a saint, and therefore does not belong to the Church, which is the communion of saints” (Church Polity, p. 6, again note the use of “the Church” over against the FV).
However, these theologians also recognized that God had commanded that believers come together for joint profession, worship, and discipline. The problem is that in this external communion many gather who are not actual believers and do not possess forgiveness of sins, union with Christ, new life, and adoption. As a result, they followed the Bible in distinguishing the Church as it appears from the Church as it really is (see Mt. 13). This is often called the visible/invisible Church distinction.
Do read through this short piece, as the visible/invisible church distinction is indeed a vital doctrine for us to grasp.