There are two kinds of particular Churches:
There are 23 such autonomous Churches, one "Western" and 22 "Eastern", a distinction by now more historical than geographical. The term sui iuris means, literally, "of their own law", or self-governing. Although all of the particular Churches espouse the same beliefs and faith, their distinction lies in their varied expression of that faith through their traditions, disciplines, and Canon law. All 23 are in communion with the Pope in Rome.
For this kind of "particular Church" the 1983 Code of Canon Law uses the unambiguous phrase "autonomous ritual Church" (in Latin Ecclesia ritualis sui iuris). The 1990 Code of Canons of the Eastern Churches, which is instead concerned principally with what the Second Vatican Council called "particular Churches or rites", has shortened this phrase to "autonomous Church" (in Latin, Ecclesia sui iuris), as in its canon 27: "A group of Christ’s faithful hierarchically linked in accordance with law and given express or tacit recognition by the supreme authority of the Church is in this Code called an autonomous Church."
Communion between particular Churches has existed since the Apostles: "Among these manifold particular expressions of the saving presence of the one Church of Christ, there are to be found, from the times of the Apostles on, those entities which are in themselves Churches (32: Cf. Ac 8:1, Ac 11:22, 1 Cor 1:2, 1 Cor 16:19, Gal 1:22, Rev 2, Rev 1:8, etc.), because, although they are particular, the universal Church becomes present in them with all its essential elements (33: Cf. PONTIFICAL BIBLICAL COMMISSION, Unité et diversité dans l'Eglise, Lib. Ed. Vaticana 1989, especially, pp. 14-28.)" (Communionis Notio, 7).
In Catholic teaching, each diocese (Latin Rite term) or eparchy (Eastern Rite term) is also a local or particular Church, though it lacks the autonomy of the particular Churches described above: "A diocese is a section of the People of God entrusted to a bishop to be guided by him with the assistance of his clergy so that, loyal to its pastor and formed by him into one community in the Holy Spirit through the Gospel and the Eucharist, it constitutes one particular church in which the one, holy, catholic and apostolic Church of Christ is truly present and active."
The 1983 Code of Canon Law, which is concerned with the Latin-Rite Church alone and so with only one autonomous particular Church, uses the term "particular Church" only in the sense of "local Church", as in its canon 373: "It is within the competence of the supreme authority alone to establish particular Churches; once they are lawfully established, the law itself gives them juridical personality."
The standard form of these local or particular Churches, each of which is headed by a bishop, is called a diocese in the Latin Church and an eparchy in the Eastern Churches. At the end of 2007, the total number of all these jurisdictional areas (or "sees") was 2,789.
Unlike "families" or "federations" of Churches formed through the grant of mutual recognition by distinct ecclesial bodies, the Catholic Church considers itself a single Church ("one Body") composed of a multitude of particular Churches, each of which, as stated, is an embodiment of the fullness of the one Catholic Church. For the particular Churches within the Catholic Church, whether autonomous ritual churches (e.g., Coptic Catholic Church, Melkite Catholic Church, Armenian Catholic Church, etc.) or dioceses (e.g., Diocese of Birmingham, Archdiocese of Chicago, etc.), are seen as not simply branches, divisions or sections of a larger body. Theologically, each is considered to be the embodiment in a particular place or for a particular community of the one, whole Catholic Church. "It is in these and formed out of them that the one and unique Catholic Church exists." 
The Holy See of Rome is seen as the central local Church. Its bishop, the Pope, is considered to be the (sole) successor of Saint Peter, the chief (or "prince") of the Apostles. Quoting the Second Vatican Council’s document Lumen Gentium, the Catechism of the Catholic Church states: "The Pope, Bishop of Rome and Peter's successor, 'is the perpetual and visible source and foundation of the unity both of the bishops and of the whole company of the faithful.'"
All the particular Catholic Churches — eastern or western, autonomous (rites) or local (dioceses or eparchies) — are by definition in full communion with the see or local particular Church of Rome.