The Orthodox Ecclesiology is the most fascinating part of the Orthodox theology. But at the same time there is no other part of the Orthodox theology with so many opinions, at some times opposite to one another. The only reliable source of the Orthodox Ecclesiology are the canons of the Church and the writings of the Saints.
Absolutely. Already, St. Jerome rebukes some bishops who think that they can "either condemn the innocent or think that they can loose the guilty. Yet in the sight of God it is not the verdict of the priests but the life of the accused that is examined. We read in Leviticus about lepers that they are commanded to show themselves to the priests and, if they have leprosy, then they are established as unclean by the priest. This does not mean that the priests make them leprous and unclean, but that they have knowledge of the leprous and the non-leprous, and they can discern who is clean and who is unclean. Therefore, just as in that passage it is the priest who "makes" the leper unclean, so also here the priest or bishop binds or looses, not those who are innocent or guilty, but because of his own office. When he hears the various kinds of sins, he knows who should be bound, and who should be loosed."
The heretics are not heretics because some bishop or council has declared them to be heretics. Analogously, the schismatics are schismatics not because a bishop has declared them schismatics. See again what St. Jerome says. Bishops and councils pronounce someone as heretic or schismatic because they know what it means to be a heretic or a schismatic. Nobody will be cut from the grace of God if bishop unlawfully proclaims him as excommunicated. And vice versa, the heretics and schismatics are cut from the Church even in case nobody cares to formally pronounce them as heretics or schismatics.
First, let me give some definitions, based on Canon 1 by St. Basil (acknowledged in Rule 2 of the Sixth Ecumenical Council (of Trullo)).
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Heretics: those who were altogether broken off and alienated from the Church in matters relating to the actual faith.
Schismatics: those who have separated for some ecclesiastical reasons and questions.
Uncanonical congregations: gatherings held by disorderly presbyters or bishops or by uninstructed laymen. As, for instance, if a man be convicted of crime, and prohibited from discharging ministerial functions, and then refuses to submit to the canons, but arrogates to himself episcopal and ministerial rights, and persons leave the Church and join him, this is unlawful assembly.
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The heretics are totally alienated from the Church. They believe in christ, but this christ is not our Christ. According to St. Basil the sacraments of the heretics are void of grace. When, however, the sacraments are performed properly by a hierarchy having a Apostolic succession, it is permissible to apply economy and to acknowledge the sacraments as valid but only after the heretics join the Church (not before).
Many schisms are due to overreaction to some unwarranted novelty in the Church, for example the New ecclesiastical Calendar, the western-style icons and western-style music in Russia, etc. There is no grace in the sacraments of the schismatics, however, we often apply economy and acknowledge the sacraments of the schismatics when they join the Church (not before).
The uncanonical congregations are not because of different opinions about doctrinal or ecclesiastical matters. These are separations caused by the human passions. We acknowledge the sacraments of these people.
It should be noted that we customarily talk about Roman Catholic Church and various Protestant Churches, although there is only one Church, the Orthodox Church and the rest are not churches. In similar way, we often apply the words "schism" and "schismatics" about uncanonical congregations. For example, we customarily call the schismatics in Ukraine schismatics, although the category "uncanonical congregations" is more appropriate for them.
1. Common faith (otherwise – heresy)
2. Mutual acknowledgement of the ecclesiastical customs (otherwise – schism)
All other separations are manifestations of bad human passions. There are even cases when it is not entirely clear which one of the arguing parts was right and which was wrong. These separations are great sins, but they do not cut from the Church. In the worst case these separations are somewhat analogous to being a member of the Church who is denied from the Eucharist due to some ecclesiastical penance.