What is the difference between the Eastern Catholic church and the Western Catholic church?
Actually, there is the Eastern ORTHODOX Church and the Eastern Rite Catholic Church.
The Eastern Orthodox Church is separated from (in "schism" with) The Catholic Church.
The Eastern Catholic Church is a "Rite"/sect in full communion with the Catholic Church and the pope. The Roman Catholic Church is the Latin Rite. Both are part of The Catholic Church.
The Eastern Orthodox Church is not, technically, part/in communion with the Catholic Church. They do not even refer to themselves as "Catholic" but rather "Orthodox."