Actually, this is not an accurate statement.
In the Eastern Catholic section of CAF, and also at Byzcath, you would be quickly corrected by someone who would tell you that ‘RITES’ is not an accurate term.
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They are Churches, each with co-equal dignity and particular set of canons. They are Sui Iuris. In fact, to
some people referring to them as rites is an insulting throwback to the days of Praestantia Ritus Latini, a now discredited policy of the pre-Vatican II church.
So there is the Byzantine Catholic Church, the Coptic Catholic Church, the Latin Catholic Church, the Syro-Malabar Catholic church and the Italo-Albanian Catholic Church (among others).
As you can see, the terminology can be confusing.
For instance (this can happen in Chicago), an Eastern Catholic might be thought of by me or you as part of the Ukrainian Catholic church, and adamantly insist that his own, the Romanian, is a separate church!
Well, yes and no. We know that in reality these are institutionally separate organizations, but in the broadest sense they are all ‘Catholic’.
This is similar to the situation in Holy Orthodoxy. In the broadest sense they are ‘Orthodox’, sharing a common belief and in communion with each other under God, but institutionally they are separated.