While it is true that one can say the Eastern Orthodox proclaims "salvation by grace through faith", the eastern understanding of what exactly salvation is departs radically from that of western Christianity. This was actually made clear in the local Orthodox Church tract another answer referenced, but seems to have been overlooked (p.78-79):
The problem is that
Orthodox and Evangelicals do not use the word saved in the same
sense. This means we are talking about different things. In the evangelical understanding the satisfaction theory of atonement is assumed.
It presupposes that the difference between the saved and the damned
is the attitude of God toward them, not any inherent quality of their
own. It also presupposes that our state of being guilty can be changed
in an instant.
For an evangelical, to be saved means to be declared “not guilty” by
God.
From the eastern perspective, western Christian confessions inherited this largely juridical interpretation of salvation, wherein Christ's death on the Cross was a key event in human history that finally accomplished retribution for man's disobedience in the Garden. While the eastern Church might have agreed with some of the motives of the Reformation (e.g. rejection of the notion of Papal primacy), it also sees that the basic premises of penal substitutionary atonement - perhaps most aptly articulated in the 11th century by Anselm of Canterbury - had been carried over.
The Archangel Gabriel announced to the Virgin that Jesus would save His people from their sins (Matthew 1:21). Elsewhere we read that the Son of Man is come to seek and to save that which was lost (Luke 19:10), that He is not come to destoy men's lives, but to save them (Luke 9:56), and that He came not to judge the world, but to save the world (John 12:47). Commenting on these passages, the late Archbishop of Dallas, Dmitry Royster, wrote:
What does "being saved" mean? From what sins do men need to be saved? Since sin in the Greek original is hamartia, literally "failure" or "missing the mark", we have to conclude that man's sin consists fundamentally in his missing the very point of his existence (although for some Christians, salvation has been reduced to nothing more than escaping the punishment of hell).1
A further contrast of Eastern Orthodox and western Christian (Roman Catholic/Protestant) fundamental beliefs concerning the nature of sin can be found in a later edition of M. Pomazansky's Orthodox Dogmatic Theology, where the editors comment:
Roman Catholic teaching on inherited guilt is based on the works of Blessed Augustine,2 who wrote "Even of believing husbands and wives are born guilty persons ... on account of original sin" ("Treatise against Two Letters of the Pelagians, Ch. 11); "The fault of our nature remains in our offspring so deeply impressed as to make it [our offspring] guilty" ("On Original Sin", Ch. 44); "Inasmuch as infants are not held bound by any sins of their own actual life, it is the guilt of original sin which is healed in them by the grace of Him Who saves them by the laver of regeneration [i.e. in Baptism]" ("On the Baptism of Infants, Ch. 24); "Until then, this remission of sins takes place in the offspring, they have within them the law of sin in such manner that it is really imputed to them as sin; in other words, with that law there is attaching to them its sentence of guilt, which holds them debtors to eternal condemnation" ("On Marriage and Concupiscence", Ch. 37). The concept of inherited guilt was affirmed at the fifth session of the [Roman Catholic] Council of Trent (1546), which, in defining the Roman teaching on original sin, referred to the "guilt of original sin." In the 17th and 18th centuries, some Roman Catholic theologians continued to develop Blessed Augustine's teaching on inherited guilt. However it was in Protestantism rather than Roman Catholicism that the doctrine of inherited guilt (also known as the doctrine of "imputed sin") was given its most extreme formulations.3
1. St. Paul's Epistle to the Romans: A Pastoral Commentary (St. Vladimir's Seminary Press, 2008), p. 33.
2. St. Augustine is venerated as a saint in the Eastern Orthodox Church, but he is also acknowledged to have committed some theological errors during the course of his vigorous condemnation of Pelagius. A fairly detailed explanation of this can be found in S. Rose, The Place of Blessed Augustine in the Orthodox Church (St. Herman of Alaska Brotherhood, 2007). Some of these Augustine himself recanted later in life.
3. Orthodox Dogmatic Theology (3rd ed.; St. Herman of Alaska Brotherhood, 2005), p.165n.