I would like some definitions of what a rite is and what a church is?
The ritual Churches
sui iuris were formerly called rites. The big change was in 1990.
In the 1983 Latin Canon Law (CIC), canon uses “Latin Church” and “ritual Church sui iuris” for Church and rite for liturgical rite, but sometimes uses rite for ritual Church.
In the 1990 CCEO Canon Law the terms rite and Church sui iuris are also defined, and are different. (e.g. rite is “liturgical, theological, spiritual and disciplinary patrimony, culture and circumstances of history,”). See below:
Can. 1 The canons of this Code regard only the Latin Church.
Can. 2 For the most part the Code does not define the rites which must be observed in celebrating liturgical actions. Therefore, liturgical laws in force until now retain their force unless one of them is contrary to the canons of the Code.
Can. 111
§1. Through the reception of baptism, the child of parents who belong to the Latin Church is enrolled in it, or, if one or the other does not belong to it, both parents have chosen by mutual agreement to have the offspring baptized in the Latin Church. If there is no mutual agreement, however, the child is enrolled in the ritual Church to which the father belongs.
§2. Anyone to be baptized who has completed the fourteenth year of age can freely choose to be baptized in the Latin Church or in another ritual Church sui iuris; in that case, the person belongs to the Church which he or she has chosen.
Can. 112
§1. After the reception of baptism, the following are enrolled in another ritual Church sui iuris:
1/ a person who has obtained permission from the Apostolic See;
2/ a spouse who, at the time of or during marriage, has declared that he or she is transferring to the ritual Church sui iuris of the other spouse; when the marriage has ended, however, the person can freely return to the Latin Church;
3/ before the completion of the fourteenth year of age, the children of those mentioned in nn. 1 and 2 as well as, in a mixed marriage, the children of the Catholic party who has legitimately transferred to another ritual Church; on completion of their fourteenth year, however, they can return to the Latin Church.
§2. The practice, however prolonged, of receiving the sacraments according to the rite of another ritual Church sui iuris does not entail enrollment in that Church.
Can. 846
§1. In celebrating the sacraments the liturgical books approved by competent authority are to be observed faithfully; accordingly, no one is to add, omit, or alter anything in them on one’s own authority.
§2. The minister is to celebrate the sacraments according to the minister’s own rite.
vatican.va/archive/ENG1104/__PC.HTM
Eastern Canon Law (CCEO 1990)
Churches Sui Iuris and Rites
Canon 27
A group of Christian faithful united by a hierarchy according to the norm of law which the supreme authority of the Church expressly or tacitly recognizes as sui iuris is called in this Code a Church sui iuris.
Canon 28
- A rite is the liturgical, theological, spiritual and disciplinary patrimony, culture and circumstances of history of a distinct people, by which its own manner of living the faith is manifested in each Church sui iuris.
- The rites treated in this code, unless otherwise stated, are those which arise from the Alexandrian, Antiochene, Armenian, Chaldean and Constantinopolitan traditions.
intratext.com/IXT/ENG1199/_PS.HTM