I assume that eastern catholicism and the Eastern Orthodox church are the same thing but I could very well be mistaken.
Is the Eastern Orthodox Church considered catholic? I have always been under the impression that their beliefs and ours are quite similar.
Are there many significant differences?
Some may disagree, but most will tell you that the most significant difference (and, ideally, the only difference) is Communion with Rome. Of course this applies to the Eastern Catholics who fall within the “Byzantine” tradition, which is the spiritual, liturgical, and theological tradition of the Eastern Orthodox. Eastern Catholics within this over-arching tradition are typically difficult to distinguish from Eastern Orthodox, aside from the aforementioned relationship with Rome and the Pope. Some have a bit more Latin influences than others, but in many cases this is in the eye of the beholder. You can attend Eastern Catholic parishes for the Sacraments, and it is considered equal to attending a Latin parish.
There are Eastern Catholics who are not so much like the Eastern Orthodox, and this is because they are from Churches that follow non-Byzantine traditions, such as the Armenian, the Coptic, the Maronite, the Chaldean-Assyrian, ect. Often these will seem as different from the Byzantine/Eastern Orthodox as the Latins, or might seem more like one or the other (I’m using Latins and Eastern Orthodox as reference points because you seem to be most familiar with them). Again, ideally the major difference between them and their non-Catholic counterparts is Communion with Rome and the Papacy. Perhaps the best Western example of the relationship between the various Orthodox Churches and the Eastern Catholics would be that of the SSPX and the Latin Catholic Church (if you’re familiar with the SSPX)
As for theological beliefs, you are correct that the Orthodox beliefs are very similar to the Latin Catholics (again, this is often in the eye of the beholder). In fact, their beliefs, aside from rejecting the Petrine Authority, are considered entirely orthodox and accepted in the Catholic Church so long as they are properly understood in a manner that is consistant with the rest of the Catholic traditions (for example, it is one thing to say that praying for the dead is approached from a different angle in the Byzantine tradition, another entirely to say that the Latins are heretics for believing in Purgatory). Many Eastern Catholics, especially clergy, study in Orthodox schools and seminaries for their theological education precisely because the theology is identical, and it allows them to focus on their own tradition rather than simply adopting the foreign (but also fully orthodox) Latin tradition which is taught in most seminaries.
Hope that helps!
Peace and God bless!
i.e. The different “Particular Churches” that are in Communion w/ The Roman Catholic Church.