Could you explain what you mean by "overlooked?" Who is overlooking the Great Schism?
Formally this split is traditionally dated to 1054, but it’s probably more accurate to say that 1054 marks a watershed moment in which the actual division was crystallised. Differences between the churches of the East and West go back well into late antiquity.
It’s worth recalling that in the first few centuries Christianity within the (Roman) Empire was mostly concentrated in the East (i.e. the Balkans and Eastward) as (a) the bulk of the population was there, (b) the historical spread of Christianity was stronger/earlier in these regions. And to recall that the Eastern half of the Empire is Greek speaking. The church in the West was Latin-speaking (though it took some time before even the church in Rome began to be dominated by Latin usage), and there were less, significant, population centres. These geographical and cultural distinctions meant that the development of theology, liturgy, and organisation in these two halves of the Empire proceeded on slightly different lines – with interaction of course, but separately nonetheless.
In the West, in particular, you see the rise and dominance of the church in Rome as a single, dominant entity, essentially holding a hierarchical position over the other churches of the West. That’s a historical development though. And the church in Rome never holds that prestige, or power, over the churches of the East, particularly centres like Jerusalem, Alexandria, Antioch, and later Constantinople. So, from early on the East has a more collegial mindset than the monarchical structure that dominates the Roman church (though even the Roman church, it must be said, did not start with a singular ‘Pope’).
Then, of course, you have the fall of the Western Roman Empire, and the church takes on a role in the post-Empire nations – among various Germanic tribal groups and kingdoms, which he East never experiences; the Eastern church essentially remains tied to the Roman state in its Byzantine development.
The Photian schism of the ninth century is a good illustration of the trajectory of relations between East and West. The patriarch of Constantinople, Ignatius, lost his position (resigned or deposed, it’s a little unclear) in 858 because he refused communion to an uncle of the emperor; Photius, a layman, was elected in his place. Supporters of Ignatius rejected Photius, since he as ordained by a bishop that had been suspended by Ignatius.
Pope Nichols sent legates to investigate, legates who, denied recognition by Ignatius, confirmed that Ignatius was rightly deposed. The Pope, though, then deposed his own legates and declared that Photius was deposed. Which, itself, is an intrusion of Roman authority. Photius himself rejected certain practices and teachings associated with the Wes, including the procession of the Holy Spirit from the Son.
In 867 a synod declared the Pope deposed. Then in late 867, Basil I took power as emperor, and reinstated Ignatius, and Photius was excommunicated. Ignatius dying in 877, Photius became patriarch again. In 879/80 Photius was reconciled with the Pope.
Why is this important? 1) It illustrates for us the rather complex interactions between Byzantine emperor, patriarch of Constantinople, and the Pope; 2) it is only one of a number of schisms between east and west, none of which were necessarily envisaged as permanent at the time; 3) it foreshadows some of the issues that became central: theologically the issue of the Spirit’s procession, ecclesially the issue of the pope’s primacy and authority.
When we come to the 11th century then, we see a conflict grow between Leo IX of Rome, and Michael Cerularius of Constantinople. This was exacerbated, no doubt, by political developments in Italy in particular, where Byzantine had lost any control. Michael argued against several Western distinctives – unleavened bread in the eucharist, compulsory celibacy in the clergy, and a few other things. Notable, the filioque clause did not appear as a major factor until after the schism in question.
Leo, for his part, objected to clerical marriage, Greeks rebaptising Latins, and the claim of authority by Constantinople over Alexandria and Antioch. Perhaps most significantly, Leo insisted that Rome was the mother church. Somewhat predictably, this led to mutual excommunications on both sides. Technically these excommunications applied to Leo (who had already died by the time the news came back) and to Michael (not the emperor or the people), and so did not constitute a break between the churches per se; and they were retrospectively cancelled in 1965; nor was 1054 necessarily seen as the start of an enduring schism at the time, but effectively it became the point that marked an ongoing division as each church continued along separate trajectories.
You have a couple questions here. I will do my best to handle each of them.
Formally, the Catholic and Orthodox Churches split in AD 1056. This is known as the Great Schism. However, the seeds of the division lay at the very origin of the Christian faith. Christianity initially spread throughout the Roman Empire, but the Roman Empire was not itself a homogeneous state. Broadly speaking, in the first centuries AD it was broken into Latin and Greek cultural halves. This later became formal, born out of Diocletian's tetrarchy. (Ironically, Diocletian implemented some of the most brutal policies of persecution against the Christians in the Roman Empire.) These separate Latin and Greek halves create, in part, the circumstances for the schism to occur.
The structure of the early Christian Church (which began referring to itself as 'Catholic' within 100 years of its formation) also helped create the circumstances for the Great Schism. Christian leadership originally stemmed from five episcopal sees: Rome, Constantinople, Antioch, Alexandria, and Jerusalem. The power and influence of these five episcopal sees is debated; for instance, the Council of Nicaea that codified many of the foundational beliefs of Christianity (found today in the Nicene Creed, prayed at Catholic masses) expressly speaks of the powers of the episcopal sees in Rome, Antioch, and Alexandria, but not the other two.
This is all to suggest that while the early Christian Church did the best it could to maintain uniformity of worship, it was extremely difficult to do so in a practical sense. Keep in mind, the Christian Church was operating over the territory of the Roman Empire, which could not govern itself from a single point, either. But one consistent element of the early Christian Church is the influence of the Roman See.
As time passes from Late Antiquity to the Early Middle Ages, several radical changes occur in the physical location of Christians. The Western Roman Empire collapses, meaning the Episcopal See of Rome is no longer in the same country with the same laws and customs as the others. Also, the rise of Islam results in the Muslims conquering Alexandria, Antioch, and Jerusalem. Thus, Rome and Constantinople were the two remaining centers of Christian leadership by the 7th century AD, and they had different intellectuals studying the Bible in different languages. Christian leadership in Rome and Constantinople come to have different understandings of the nature of God and the Trinity over time. The Catholic Church in Rome believes that God the Father, the Son, and the Holy Spirit have always existed in an equal format. The Orthodox Church believes God the Son and the Holy Spirit emanate forth from God the Father. This changes the way humanity interacts with and situates in relation to God. Also, Constantinople rejected Papal Primacy, meaning that they do not consider the Pope to be the leader of all Christians.
While this may, on the surface, seem like splitting hairs or be superficial, the nature of the Trinity and Papal Primacy have very deep theological implications that I am not qualified or intelligent enough to speak on.
As for similarities, they hold more in common with each other than they do with the Protestant Christian faiths. Again, I am not extremely familiar with the intricacies of Orthodox theology, but both the Catholic and Orthodox churches believe in the transubstantiation of the Eucharist, meaning that they both believe the Eucharist is Christ, although they each have their own nuances in their understanding of the Eucharist as Christ. This separates them from Protestantism, which rejects transubstantiation.
I hope that answers your question well enough. One more thing: the reason the Great Schism is 'overlooked' in the west is because, simply, the Orthodox Church does not have the numbers of faithful or the cultural impact to be highly visible. Meanwhile, part of the American foundational myth is based upon flight from religious persecution in England, an extension of the Protestant Reformation.
Source: Chadwick, Henry. East and West: The Making of a Rift in the Church: From Apostolic Times Until the Council of Florence. Oxford Press. 2003.