Hello there!
In 1054 AD, the one Church split into two similar branches of it. This is because the Pope at the time, Pope Leo III, crowned Charlemagne the Holy Roman Emperor in the year 800. This event, in turn caused tensions to arise.
The Byzantine Empire was the only remaining trace of the Roman Empire. This crowning essentially "de-legitimized" the Church's recognition of the Byzantine Empire, as the Pope called Charlemagne the emperor of the Roman Empire.
In 1054, a formal split was established, thus creating Greek Orthodox Church, and the Roman Catholic Church.
I hope this helps and clarifies a bit!
Brady