Short answers, pulled from the story.
Greek East and Latin West were terms that originally distinguished the Greek-speaking Eastern Mediterranean from the Latin-speaking Western Mediterranean within the Roman Empire. They later came to describe the division of Chalcedonian Christianity between the Eastern Orthodox peoples of the Byzantine Empire and the Roman Catholic peoples of Western Europe.
Theologian Andrew Louth placed the transition between 681 (the Third Council of Constantinople) and 1071 (the Battle of Manzikert), attributing it primarily to the rise of Islam and the Arab disruption of Mediterranean stability in the seventh century. The formal East-West Schism is dated to 1054, though Louth considered that year of little importance to contemporaries, arguing it gained significance mainly in relation to the Councils of Lyon in 1245 and 1274.
By the twelfth century, theological debate between the Greek East and Latin West focused on the filioque controversy regarding the procession of the Holy Spirit, the question of leavened or unleavened bread in the Eucharist, and the primacy of the pope.
Greek had spread across the Eastern Mediterranean as a lingua franca through centuries of Hellenization, particularly during the Hellenistic period, long before Rome absorbed those territories. Although Latin held official status from the beginnings of the Roman state, Romanization was considerably less prominent in the east, and Latin's usage ultimately declined relative to Greek.
Marcus Aurelius wrote the Meditations in Greek, composing the work around 170. Roman emperors who spoke Latin tended to learn Greek, but the reverse was rarely true.
The Western Empire collapsed in 476. This collapse accelerated the Greek-Latin divide that had been building through administrative changes between the third and seventh centuries, leaving the Eastern Roman (Byzantine) Empire to carry on until its own fall in 1453.