The Eastern Orthodox understanding of grace is radically different from that of Roman Catholicism.
Firstly, Roman Catholic theology maintains that grace is something that is created. The Catholic Encyclopedia states:
[Grace] is not a substance that exists by itself, or apart from the
soul; therefore it is a physical accident inhering in the soul (1911
ed., vol. 6, p. 705)
It furthmore states:
Sanctifying grace may be philosophically termed a 'permanent,
supernatural quality of the soul' (ibid.)
In contrast, Orthodox theology maintains:
Grace is the Uncreated Energy of God Himself, which at the time of
man’s creation was intimately connected with his soul. Man
participated in the Divine life through the Divine Energy, and this
participation was proper to the original nature of man.
Hieromonk Damascene, note in Orthodox Dogmatic Theology (3rd ed.), by Protopresbyter Michael Pomazansky,
p. 166.
Orthodox theologian Vladimir Lossky further explains the difference in understanding in his book, The Mystical Theology of the Eastern Church:
That which western theology calls by the name of the supernatural
signifies for the East the uncreated — the divine energies ineffably
distinct from the essence of God. The difference consists in the fact
that the western conception of grace implies the idea of causality,
grace being represented as an effect of the divine Cause, exactly as
in the act of creation; while for eastern theology there is a natural
procession, the energies, shining forth eternally from the divine
essence. It is in creation alone that God acts as cause, in producing
a new subject called to participate in the divine fullness; preserving
it, saving it, granting grace to it, and guiding it towards its final
goal. In the energies He is, He exists, He eternally manifests
Himself.
Kindle Locations 1532-1541
This difference in understandings of grace leads to radically different understandings of the nature of sin and salvation in both traditions. As monk Damascene further comments:
In Roman Catholic teaching original sin consists only in the privation
of sanctifying grace (also called “original justice”), while the
nature of man remained the same after the fall as it had been before
the fall. In this view, the nature of man has not become corrupted;
rather, the privation of grace in itself constitutes “a stain, a moral
deformity” (Catholic Encyclopedia, vol. 11, p. 314). According to
Orthodox theology, on the other hand, man’s nature was corrupted at
the fall, and this corruption caused man to lose the indwelling of
Grace and deprived him of participation in God. As Vladimir Lossky
notes, “The deprivation of Grace is not the cause, but rather the
consequence of the decadence of our nature” (Mystical Theology, p.
132).
Salvation, in the Orthodox understanding, is a healing of man ("heal" and "save" are the same word in Greek), and involves cooperation of man with God to participate in His grace. It is not so much a restitution, as a restoration. Sin is seen not as an act or series of acts that offend God, but rather as a state of being separated from God. It is interesting to note that the verb form of the Greek word for sin - hamartia - is used in ancient Greek to describe what happens when a warrior misses their target ("misses the mark"). In his commentary on Romans, the late Archbishop Dmitry Royster (a Baptist convert to Orthodoxy) wrote:
What does "being saved" mean? From what sins do men need to be saved?
[Matthew 1:21]. 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).
St. Paul's Epistle to the Romans: A Pastoral Commentary, p. 33