jimmy:
There are 22 rites in the Catholic Church. They all believe the same thing but the follow different traditions(with a small t). The The Latine Rite are the Roman Catholics. In the Byzantine rite the priests can get married.
The people who go to the Latin mass are Latin rite Catholics, which are the Roman Catholics. You coulld only call them orthodox in that they are orthodox in faith meaning true. They are not Eastern Orthodox.
You must be careful when thinking of the different rites. They are not different branches, they are the same church, they just have a different liturgy and some different customs. They believe the same exact faith and all rites follow the Pope.
My brother Michael (Hesychios) spoke to some of the differences in doctrinal expression and understanding. Let me address a few other misconceptions regarding the Eastern Churches.
There are 23 Churches
sui iuris (not rites) that, together, constitute the Catholic Church - 1 Western and 21 Eastern. The term
sui iuris means, literally, “of their own law”, or self-governing. All 23 are in communion with Rome. The most well-known and largest is the Latin Church, the one I referred to as Western. (Note that the Latin Church includes not only those who attend sanctioned Latin Masses, but also those who attend the Novus Ordo Mass in the vernacular).
The 22 Eastern Catholic Churches use 5 (or 6, depending on how one breaks down the distinctions) different Rites among them. The largest group use the Byzantine Rite.
Eastern Catholic Churches generally represent bodies of persons who entered into communion with Rome from the Eastern or Oriental Orthodox Churches. As a consequence, there is a counterpart Eastern or Oriental Orthodox Church to every Eastern Catholic Church except two - the Maronite and Italo-Grieco-Albanian Byzantine Catholic Churches, neither of which were ever separated from Rome. (You will occasionally see assertions that some other Eastern Catholics never left communion with Rome, but those claims aren’t fully supported by historical fact.)
Strictly speaking, the Churches that utilize the Byzantine Rite are the Eastern Catholic Churches; the others are the Oriental Catholic Churches. This distinction reflects one that is made among our counterpart or Sister (Orthodox) Churches, where Eastern Orthodox and Oriental Orthodox Churches are also distinguished by the Rite that each uses.
Originally, there were 3 Rites - Latin, Alexandrean, and Antiochene; the Byzantine (or Constantinoplian) Rite was added thereafter. These arose from the customs and style of worship in what were then the four most important Christian centers. The differences among them sprung from the fact that uniformity of worship and liturgical practice was difficult to maintain over time, as the number of clergy increased, local cultures and customs began to be woven into the rituals used, and both travel and communication were hampered by geography and the limited means available to make and maintain contact between churches and clerics.
Over time, the four were modified or developed further in new regions. Some variations were so distinctive as to be deemed separate Rites. The Maronite and Armenian Rites, both developed in relative isolation because of geography. The result is that most authorities term the Maronite as a Rite unto itself; while a minority place it within the West Syrian Tradition of the Antiochene Rite, where it originated. As to the Armenian, it is almost invariably deemed a separate Rite; it is uncommon to see it categorized within the Byzantine Rite, where it originated.
See:
forums.catholic-questions.org/showthread.php?p=112157#post112157 and the 3 or 4 posts immediately following for a breakdown of the Eastern Catholic Churches by Rites, Traditions, hierarchical structure, etc.
Many years,
Neil