What is the eastern Catholic and Eastern Orthodox understanding of mortal and venial sin? In western Catholicism, there is an idea that if you commit a grave sin with full consent and full knowledge that it is grave, it becomes a mortal sin. You loose your state of grace and are set on a trajectory for Hell. You are forbidden to receive the Eucharist unless you go to confession.

I'm wondering what the eastern Christian understanding is, particularly eastern Catholic, because they are bound to accept the mortal/venial sin distinction but I understand they don't emphasize it in the same way as western Catholics do. What is the eastern understanding of mortal sin?
There is no such distinction between &quot;mortal&quot; and &quot;venial&quot; sin in the fashion you suggest within the Eastern Orthodox Church, but it must also be understood that sin, as well as the related concepts of grace and free will, is understood completely differently in the Orthodox Church.
Sin, within the Eastern Orthodox Church, is seen as a spiritual disease - a disease that we inherit as a result of man's Fall in Paradise.  It is seen more as a sickness to be treated than a crime to be punished.
A dogmatic definition of &quot;sin&quot; is provided in John's first Epistle - the definition that also appears in one of the few formal &quot;catechisms&quot; of the Orthodox Church (The Longer Catechism of Philaret, Metropolitan of Moscow):  αμαρτια εστιν η ανομια - &quot;sin is lawlessness&quot; (1 John 3:4).  In the Latin: peccatum est iniquitas - &quot;sin is iniquity&quot;.
Venerable Bede (672-735), who is considered a Church Father in both the Eastern Orthodox and Roman Catholic Church writes:

The force of this thought is grasped more easily in the Greek language
in which the Letter is written, since in that language iniquity is
called ἀνομία, which implies something done, as it were, against the
law or without the law, since in Greek νόμος means law.  When John
says therefore, Everyone who commits sin also commits iniquity, that
is, ἀνομίαν, and sin is iniquity, he clearly suggests that by every
single sin we act against the law of God, according to the saying of
the Psalmist, I have counted all sinners on earth as transgressors
[Psalm 118:119 LLX].  For all who commit sin are guilty of
transgression, that is, not only those who reject the known precepts
of the written law which have been given them, but also those who
whether through weakness or negligence or even ignorance destroy the
innocence of the natural law which we received in the first-created
man.
Commentary on the Seven Catholic Epistles (tr. Dom David
Hurst), pp.187-188

The Orthodox Christian monk and theologian Justin Popović (1894-1979) further explains this as follows:

Sin defiles man and his being, which is in the divine image of God and God-given.  It is the fundamental impurity, proto-impurity, and
the origin of all impurities.  Purity is, in reality, purity from sin
and its impurities.  That is holiness.
For such purity, such holy purity, is the divine law of man's being.
This purity is achieved and maintained by living in goodness in love,
in prayer, in righteousness, in meekness, in fasting, in
self-restraint, and in the rest of the virtues of the Gospel - simply
put, in holiness, conceived of as the synthesis and unity of all the
holy virtues and grace-filled energies.  In opposition to purity, to
holiness as law, to the divine law of man's being, stands sin as the
first and fundamental lawlessness.
Commentary on the Epistles of St. John the Theologian, p.39

While certain sinful acts - which we might refer to as specific &quot;sins&quot; - reflect a graver spiritual condition than others, there is really no systematic categorization of them as exists within the Roman Catholic Church.
I cannot really comment on the doctrine on sin that Uniates hold, but I would be surprised if it held to Eastern Orthodox rather than Roman Catholic doctrine.  The two theologies are quite distinct.  I am assuming that if there is a lighter emphasis on the mortal/venial distinction it is a residual influence of Eastern Orthodoxy.
(As a footnote, I attended high school at the Benedictine Abbey where Dom David, the translator of Bede's commentary above, was a novice at the time.  I was surprised to encounter him in print decades later as an Orthodox convert).