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Ghosty
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Rite is not to be confused with Church. The Rite is the liturgy that a given Church practices, a Church is a unit headed by a Patriarch. The Latin Church is headed by the Patriarch John Paul II and practices the Roman Rite under most circumstances. There was a time, before Trent, when there were many Rites practiced in the Latin Church (such as the Mozarabic and Carmelite Rites). Here’s a page on EWTN’s website that has a decent, though not exhaustive, explaination of these matters:
ewtn.com/expert/answers/catholic_rites_and_churches.htm
ewtn.com/expert/answers/catholic_rites_and_churches.htm