Yes, that's correct. The Roman Catholic Church is led by the Pope, who resides in Vatican City and has spiritual authority over Catholics worldwide. The Byzantine Empire, which was a significant center of Eastern Orthodoxy, fell in 1453, and since then, the structure of the Eastern Orthodox Church has evolved differently.
Instead of a single leader analogous to the pope, the Eastern Orthodox Church is composed of several autocephalous (self-governing) churches, each led by its own bishop or patriarch. For example, the Ecumenical Patriarch of Constantinople is considered the "first among equals" among Orthodox bishops, but does not wield the same authority as the Pope in the Catholic Church. Each national church, such as the Russian Orthodox Church, the Greek Orthodox Church, or the Serbian Orthodox Church, governs its own affairs while maintaining a shared theological foundation and communion with one another. This structure reflects a diverse and decentralized approach to church leadership in the Eastern Orthodox tradition.