Well, first of all, a disclaimer: I know a lot about Eastern Orthodox theology, not Eastern Catholic. So, I’ll give you a rundown on the Orthodox stuff. I’d appreciate if any ECs here could run over it and tell me what’s accurate for them and what’s not.
Essentially, the core concept to understand is thabt there’s a profound difference between Western theology (Meaning both the Protestant and Catholic theology - they’re viewed as one and the same in the East because the Protestant theology developed out of Catholic theology, as much as Protestants might not like to admit it). Eastern theology developed seperately, and in a whole different world. Western theology comes mostly from St. Aquinas, St. Anselm (both of whom are post-schism saints) and St. Augustine (who was never really popular in the East). The really big difference is St. Anselm, and his concepts of justification and satisfaction. This leads to a more legalistic approach to sin, where mankind lives in a constant “debt” to God because of his sins and must repent for them in order to satisfy God and avoid his wrath, and the dread judgment before God is something of a legalistic affair as well, with God judging his good deeds and bad deeds and either granting him entry into heaven and eternal paradise, or hell and eternal torment. (which is not really an accurate description at all, but that’s how it’s viewed in the East). Easterners never had such a concept. They believe in a concept called theosis, “deification”, which was mainly defined by Gregory Palamas, although it goes as far back as St. Athanasius (some even claim references to it in the NT epistles, but I don’t know enough there to comment on that claim). Essentially, in theosis, God is divided into two properties - his “essence”, which is the unknowable “substance” of God, and his “energies” which are the physical manifestations of God. These energies are often symbolized by a fire, and It is believed that man can partake in these “energies” of God, while still remaining man and not sharing with the “substance” of God. Just as the burning bush was overcome by the fire of God’s presence and yet was not consumed by it, still remaining a bush. Or, another great example commonly used by the Church Fathers is that of a nail, which when put into a forge obtains the properties of the fire, becoming red-hot, while still remaining in substance a nail. The Orthodox believe that the “light” of God is actually this fiery “energy” - the light that illumined Jesus during the Transfiguration, for instance. According to Theosis, man should attempt to become as much like God as he possibly can, and when he does so, he becomes a partaker in these energies of God. When you hear Easterners take about Saints with illumined faces, this is what they’re talking about. And when a man dies, he passes into God’s fiery energies, and becomes glorified like him by these energies. Those who die having gone against God, however, will still pass into the fire, but because he rejected God this presence of God will become as a fire eternally tormenting him. This is the Orthodox Hell. As St. Athanasius put it - God became Man so that Man might become God.
That’s a very simplistic explanation of it - obviously it’s impossible to sum up an entire theological system in one paragraph. But that’s the gist of the main difference between Orthodox and Western theology. Besides that, the two are mostly identical.
If you’re looking to explore it further, I’d recommend the book “The Mystical Theology of the Eastern Church”, by Vladimir Lossky. It’s an Orthodox, not EC book so take it with a grain of salt. But it explains the system quite well.
Again - this is all Orthodox theology - I don’t know where EC theology differs from it.