Make Generalizations. What led to the creation of two different Christian societies in Europe?

I believe it was the division of Byzantium and the Latin West. Byzantium was the emperor of Constantinople the area around Greece and Turkey and North into Russia. Latin West was under the control of different people until dominance of the Franks in the region. Another powerful and well noted authority was the Pope. Basically ... there was a the decline of Rome and different views on the Christian doctrine. (Q_Q) That's the best way I can word it.