the Eastern Orthodox Church and the Roman Catholic Church

I don't know if you should put it that way, try this: The Eastern Rite Churches are all part of the Catholic Church.

Chrismation.

The two churches were the Eastern Orthodox and the Roman Catholic

The term "catholic" is claimed by both the Roman Catholic Church and the Eastern Orthodox Church. The Roman Catholic Church includes all the Churches that accept the authority of the pope in Rome, including certain Eastern Churches. The Eastern Orthodox Church does not accept the authority of the pope in Rome.

The pope is the spiritual leader of all Christians. However, the Protestants and Orthodox do not recognize that leadership.