Final answer:
The Western Church, or the Roman Catholic Church, spread Christianity in the West, helped convert Germanic peoples and sent missionaries to various continents. The Eastern Church, known as the Eastern Orthodox Church after the Great Schism, spread Christianity throughout the Byzantine Empire and to Eastern Europe and Russia.
Step-by-step explanation:
The roles that the eastern and western churches played in spreading Christianity were quite significant and distinct from each other. The Western Church, identified as the Roman Catholic Church, was pivotal in uniting Western Europe and providing a sense of European identity after the fall of the western Roman empire. It played a key role in converting the Germanic peoples to Christianity, preserving the classical tradition, and supporting the new rulers to legitimize their rule and christianize their populations. The Western Church eventually spread Christianity through missionary work, especially after the establishment of the Jesuit order, which sent missionaries into Asia, North and South America, and Africa, often in conjunction with European colonial expansion.
The Eastern Church, which became known as the Eastern Orthodox Church after the Great Schism in 1054, helped spread Christianity throughout the Byzantine Empire and beyond. It maintained its center in Constantinople and used the Greek language for its services. This branch of Christianity was very influential in spreading the faith to the Slavic lands of Eastern Europe and Russia, and today includes multiple national Orthodox churches, such as the Greek Orthodox and Russian Orthodox churches.