Generally the "Oriental Catholics" are the Syriac Catholics, Maronites, Copts, Syro-Malankara, Armenian Catholics, Ethiopian/Eritrean Catholics, and loosely the Chaldean and Syro-Malabar Catholics although the latter two would fall into a different family of Tradition to be perfectly accurate.
These are somewhat different in their theology and tradition that the "Eastern Orthodox" or "Byzantine Churches". The Syriac and Armenian Churches for example, do not necessarily hold a position of Supreme Authority by a Patriarch or Pope to be lacking as the Byzantine's usually do. Also, the theology of Essences and Energies are not dogmatic as in Eastern Orthodox/Byzantine Catholicism. The theology of the Immaculate Conception, even as defined by the Latin scholastic terminology, is not necessarily problematic. Most of these Churches also hold a Miaphysite view of Christology. These Churches also do not have one singular shared Liturgy and are more open to diversity in expression. They also sometimes openly have Saints, who in their lifetime, were adversarial toward each other.
Culturally, the "Oriental" Catholics and Orthodox maintain much more of the older Jewish cultural traditions (many don't each pork for example, men/women sit separately in Church, etc) and other local variants because they are ethnic descendants of those people; and are also more Semitic, rather than Greek or Latin in culture.
Ok, when you said, "The Syriac and Armenian Churches for example, do not necessarily hold a position of Supreme Authority by a Patriarch or Pope to be lacking as the Byzantine's usually do." You mean the Syriac and Armenian Orthodox? Please teach me about this. If you meant (Oriental) Orthodox, did you mean like the Catholicos of All Armnians and like how the Copts have a Pope Shenouda some-number or is there something else with the petrine see that is going on? When you say Byzantines usually hold it to be lacking, this is the Eastern Orthodox? I thought they held that the Pope was first among equals but would not submit to him and thus were not in the Catholic Church and if you meant Byzantine Catholics, well, they are under the Pope. Who holds is lacking and how and who does not hold it lacking and why?
"Also, the theology of Essences and Energies are not dogmatic as in Eastern Orthodox/Byzantine Catholicism."
Essences and energies?
Weird fact about the Armenians: Traditional Armenian cooking has no pork. Armenians are non-semitic and have had a lot in common with the Greeks, yet have a 20% chance of having the Cohen genome in them according to some online research I have done.
