In what ways did the Eastern Empire change from the Western Empire?

I will assume the question concerns the Roman Empire.

The Roman Empire grew vast and became harder to manage from Rome. This forced Emperor Diocletian to divide the Empire into two manageable territories, the Eastern and Western Roman Empires. The Western Empire maintained the administration center in Rome, while the Eastern Empire established Byzantium/Constantinople as its administrative center. However, after the dissolution of the Greater Roman Empire, the Eastern Empire developed its own character. The Eastern Empire adopted Greek over the traditionally established Latin. Christianity was established as the Empire's official religion and other religious practices including the traditional Roman pagan practices were declared illegal. The Eastern Empire also sought to ban Iconoclasm (worship of religious icons and imagery). The situation caused the continued rift between the Western and Eastern Empires religiously and politically.