The worldwide Catholic Church is made up of 22 autonomous “particular Churches”, of which the Latin Church is the biggest (about 90% of all Catholics are Latin or “Western”). Each Church has its own laws, but all agree on the fundamentals of Catholic dogma and are in communion with the Bishop of Rome.
After the Latin Church, the various Churches who follow the Byzantine Rite are the most common. These include the Ukrainians, the Melkites, and the Ruthenians, among others. As mentioned, these Churches do not include the “and the Son” clause in the Creed, but that does not mean they do not agree with the western understanding of it. In Latin the term used (Filioque) is ambiguous and can be understood in an orthodox way. It was added to the Creed (outside of an Ecumenical Council) in order to fight off Arian heretics, and Rome eventually came to adopt it, yet without forcing the other Churches to adopt it as well.
In Greek, however, it is very difficult to translate Filioque properly in a way that is orthodox, because the meaning changes. This is another reason why the Greek Churches don’t include it their version (which is actually the original version) of the Creed.
There are other differences between Latins and Easterns… Latins, Maronites and Armenians use unleavened bread in the Eucharist, whereas Byzantines use leavened bread. In the Byzantine tradition, infants are baptised, confirmed and given First Eucharist immediately. In the Latin Church, infants are only baptised, and then when they are older they receive the other two sacraments. In the Latin tradition, Mary being bodily taken up into Heaven is called the Assumption, whereas in the Byzantine tradition it is called the Dormition. The liturgy itself is called the Mass in the Latin Church, but in the Byzantine Churches this term is not used, instead they most often call it the Divine Liturgy.
Catholics can always receive Communion, Confession and the Anointing of the Sick from any Church they attend, whether Latin or Eastern, as long as the Church is in union with Rome. I myself (a Latin) have attended numerous Byzantine liturgies and received the Eucharist there.
If you have any more questions, please do not hesitate to ask
Hope all this helps!
