The Eastern Catholic Churches are 23 sui juris Churches who are in full communion with Rome, the Eastern Orthodox, on the other hand, are not and find their unity at Constantinople.
There is really only one disagreement at the doctrinal level between Catholics and Eastern Orthodox and that is over the nature of the papal supremacy. The other “disagreements” aren’t really disagreements but mostly different traditions of the western and eastern churches.
Both Eastern Orthodox and Byzantine Eastern Catholics hold to the Byzantine view of purgatory which is a completely acceptable theological point of view within the Church. They see purgatory as a state of final theosis where one completes their journey with God and achieves unity with him, hereby entering into a heavenly state before the universal resurrection of the dead.
The Latin conception of purgatory sees it as a state where a soul who has died in a state of grace but still need purification and undergoes a suffering to achieve this. After purification, one may experience the beatific vision in heaven awaiting the universal resurrection of the dead.
As for unleavened and leaved bread, Eastern Orthodox and many Eastern Catholic Churches use leavened bread as this symbolizes the resurrection of Christ. This is the tradition of the eastern Churches and is fully valid. Christ is as present in the eastern Eucharist as he is in the western Eucharist.
The Latin Church primarily uses unleavened bread as Jesus originally used and as the early Church did, but as said, leavened bread is perfectly valid. This is the tradition of the west.
Lastly, in regards to the filioque, this also is not a theological difference. Some Eastern Orthodox try to make it that way, but it’s really an issue of semantics rather than actual doctrine. Both the Catholic and the Eastern Orthodox Church believe in the same thing in regards to the procession of the Holy Spirit as defined in the 17th Ecumenical Council of Florence and Basel (1431-1449). Many Eastern Catholic Churches continue to follow their traditions and may not include the filioque in their version of the Nicene creed.
“The Greeks asserted that when they claim that the holy Spirit proceeds from the Father, they do not intend to exclude the Son; but because it seemed to them that the Latins assert that the holy Spirit proceeds from the Father and the Son as from two principles and two spirations, they refrained from saying that the holy Spirit proceeds from the Father and the Son. The Latins asserted that they say the holy Spirit proceeds from the Father and the Son not with the intention of excluding the Father from being the source and principle of all deity, that is of the Son and of the holy Spirit, nor to imply that the Son does not receive from the Father, because the holy Spirit proceeds from the Son, nor that they posit two principles or two spirations; but they assert that there is only one principle and a single spiration of the holy Spirit, as they have asserted hitherto. Since, then, one and the same meaning resulted from all this, they unanimously agreed and consented to the following holy and God-pleasing union, in the same sense and with one mind.”
- ECUMENICAL COUNCIL OF FLORENCE (Session 6)
Now, the majority of the Eastern Catholic Churches were out of communion with Rome at one time, and this includes the major Churches like the Ukrainian Greek Catholic Church which was first united to Rome at the Union of Brest (1595-1596) after breaking from the rest of the Eastern Orthodox Church. Every Eastern Catholic Church has a long and complex and ancient history and you can read about each online.
The only Church that never broke from Rome is the Maronite Church, which was never technically out of communion with, although they were very isolated for a number of years and may have held to Monothelitism at one point. They were rediscovered during the crusades and submitted willingly to Rome leaving behind any heresy they might have once held onto.
The Italo-Albanian Greek Catholic Church, a Byzantine Catholic Church, also is technically an exception to this because they never split from Rome. The Byzantine church in southern Italy and Sicily was made up of primarily Greek Christians who inhabited the area after originating during the time when the Byzantine empire controlled that area. They had a influx of Albanians during the 15th century, hence the “Italo-Albanian” part. They weren’t always sui juris though, and were under the control of Latin bishops at one time, while still retaining their Byzantine traditions and liturgy, the same found in other Byzantine Catholic and Eastern Orthodox Churches.
