What are the organizational and administrative differences between how the Anglican ordinariate works and how the Eastern Catholic Churches are structured? I know that they are quite different, but for the life of me, I can’t seem to put my finger on the differences.
The Anglican Ordinariate (Roman Catholic Ordinariate to the Chair of St. Peter) is in line with the Western Church and its teachings. You will find the differences the same as those between the Eastern Church and the Western Church. This pertains to the liturgy though. It may give you a direction to head in though.
The Anglican Ordinariates are canonical structures that exist within the Latin Church. The Catholic Church is a communion of sister Churches sui iuris (of their own law) - the Latin Church is one of those churches (and by far the largest). In theory, the 20+ Eastern Catholic Churches are each equal in dignity with the Latin Church. (Though in practice, only the Eastern Churches of patriarchal and major archepiscopal status, of which there are 10, have full autonomy - the others depend upon Rome for the appointment of bishops and other fundamental matters). An Eastern Church of patriarchal status, such as the Melkite Greek Catholic Church, is able to promulgate its own particular laws, regulate its own liturgy, and elect its own bishops/patriarch. None of the Eastern Churches are bound by the Latin Code of Canon Law.
The Ordinariates, on the other hand, are subject to the Latin Code of Canon Law and are completely dependent upon Rome. While they do have their own unique liturgy and there are special provisions that govern them (such as the ordination of married men to the priesthood), each of these unique provisions is granted by Rome and each married man ordained to the priesthood receives a specific dispensation from Rome. Further more, at present, the three men who serve as Anglican Ordinaries (in the UK, North America, and Australia), are married men and thus only priests, not bishops - which means that theologically their authority of jurisdiction is a delegation from Rome. Essentially, the Ordinariates are dioceses of the Latin Church, like any other diocese, but with special privileges. In the Archdiocese of Milan, which is also part of the Latin Church, the Ambrosian Rite is celebrated in some churches in place of the Roman Rite. Finally, it should be noted that Anglican Ordinariate priests, as priests of the Latin Church, can always celebrate the Ordinary and Extraordinary Forms of the Roman Rite even if they are also permitted, by particular law, to celebrate the Anglican Use.
It gets confusing because people forget that the Latin Church is just another Church sui iuris, like her sister Eastern Churches. The Latin Church is so vast and historically, due to the tragic schism with most of Eastern Christendom, comprised virtually the entire Catholic Church for many centuries. It is important to remember that the Pope of Rome, while head of the entire Catholic Church, is also specifically the head of the Latin Church, just as he is also specifically head of the Roman diocese, and often acts in that capacity without any bearing on the Eastern Churches.
That's very helpful. Thank you.