All I know is that our Purgatory (EO) is better than their Purgatory (RC). 
How can you have a purgatory if you guys claim you don't believe in it? 
You did see the grinning face, right? (Which means I was being tongue-in-cheek).
Ok, ok, I should've put the first "Purgatory" in quotation marks; since we just call it "the intermediate state".
Both names, "Purgatory" and "Intermediate state", come from the early Church Fathers. They taught that:
-There is an INTERMEDIATE STATE between heaven and hell.
-Those people who die without bearing the fruits of repentance for mortal sins, or who have small sins unconfessed, are confined in hell temporarily (not to be tormented but as if in jail) to be PURGED (cleansed) of their passions. After a time, and through the prayers of the Church, and good deeds done on earth in their name, they enter heaven.
-The Old Testament Patriarchs and prophets were confined in a similar way, and were released by Christ after the Crucifixion.
-At the last judgement, the INTERMEDIATE STATE will be abolished, and those in it will go to heaven.
-This doesn't help the unrepentant sinners, of course. They stay in hell.
BTW, unbaptised babies who die go to heaven. Those who are unbaptised and old enough to know good from evil (starting around age 6-7) when they die, their fate is in God's hands. But we Orthodox trust in God's love. Surely He can find some room in the intermediate state for the good ones.
Where our beliefs differ from those of the RCC are the following:
1- There is no fire in purga - sorry, the intermediate state. There is only the near-absence of divine light.
Heaven-------------> Divine Light
Intermediate State -> Very little Divine Light. Mostly Darkness.
Hell-----------------> No light, but burning Fire
2- The Divine Light and the fire of hell are not temporal, created things. They are both the uncreated grace/energy/will/activity of God.
3- There is no punishment in purga - sorry, the intermediate state. The people confined there have already been essentially forgiven. God does not forgive and punish at the same time. Its illogical. Also, God does not NEED to be satisfied in any way. He does not NEED anything. He is the only truly FREE Being. In His freedom, He can choose to forgive. Once He forgives, He does not need to punish afterwards. The purpose of purga - sorry, the intermediate state, is not to punish, but to give one some time to distance oneself from the passions which attach us to this life, so he could enter heaven. Its a second chance, not an obstacle.
4- Concerning indulgences, I will quote Fr. John Romanides:
the Orthodox Church vigorously condemned all magical understandings of salvation which might conceive of the saving grace or energy of God as something created, stored quantitatively within a so-called bank of grace, and distributed quantitatively through sacramental acts and indulgences, by proclaiming the biblical and patristic teaching that God Himself saves men directly by His own uncreated energy. The very basis of all Orthodox doctrine concerning Trinity, Christology, Ecclesiology, and Soteriology is the fact that God creates, sustains, and saves creation not by created means, but by His Own life-giving energy. Only God can be the source and subject of His uncreated energies.
The divine energies are neither the essence of God (God is not actus purus), for this would mean that God acts by essence and not by will (pantheism), nor hypostatic (individual entities), for this would either reduce God to a mere platonic conglomeration of ideas, or to a neo-platonic source of emanating creatures, thereby confusing the Son and the Spirit with such creatures. (A good example of such views concerning divine energies may be found in the teachings of the heretics attacked by St. Irenaeus.)
The divine energies are not creatures, but precisely the creating, life-giving, justifying, uncreated energy of God. [ 19 ]
Therefore grace cannot be manipulated and distributed by man who can only partake of this uncreated light of God in the corporate life of selfless love in the flesh of Christ locally manifested and formed by God Himself in real people epi to auto (in the same place).
-The Ecclesiology of St. Ignatios of Antioch (paragraph divisions and emphases are mine)
(
http://www.romanity.org/htm/rom.11.en.the_ecclesiology_of_st._ignatius_of_antioch.01.htm)
In the RCC, salvation is a reward for faith and good works, or "merits".
In most Protestant Churches - except Calvinists - salvation is a reward for faith.
In Calvinism, salvation comes by winning a Divine lottery.
In Orthodoxy, God does not save or condemn on a whim, and neither does He work from a reward-and-punishment system. Rather, salvation or damnation are a kind of "tendency" which depends on how we use our free will. If I let go of an object, it will tend to move towards the earth's center faster and faster. The earth is not rewarding it or punishing it. That's simply the nature of gravity. If my free will is always cooperating with God's grace/uncreated light, I will develop a tendency towards heaven. If my free will usually does not cooperate with God's grace, I will develop a tendency towards hell. There is no reward-and-punishment.
Therefore, God does not need to dip into a bank-account of superabundant merits, to withdraw created grace, and give it to us in indulgences. He has an endless supply of uncreated grace from Himself. The way we "complete" the work of Christ is, simply by cooperating with that grace. Nor does He need to remit punishment that would be given after forgiveness, since, as I mentioned above, such punishment does not exist. The penances after confession, and acts of charity or piety (fasting, prayers, etc.) that we do, are not meant to satisfy God's justice or grant us rewards. They simply train us to control our passions by cooperating with God's grace, in order to develop selfless love and acquire a tendency towards heaven.
5- This isn't specific to purgatory, but its still important. The saints in heaven experience plenty of joy and light. But after the resurrection, they will experience still more, once they are reunited with their bodies. Heaven is not static, but dynamic. Saints always move "from Glory to Glory" (St. Gregory of Nyssa). Only hell is static.
(And, yes our purgatory is better than your purgatory.

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