The same name can refer to different churches / communities…
Coptic Church was founded, according to tradition, by St. Mark.
Coptic Orthodox Church of Alexandria: schismatic since 451 AD
Coptic Catholic Church: in full communion with Rome, under Coptic Catholic Patriarch of Alexandria Ibrahim Isaac Sidrak
Ethiopian Orthodox Tewahedo Church: separated in 1959 from the Coptic Orthodox Church of Alexandria, which in turn was in schism since 451 AD, and is thus also in schism.
Church of the East (aka Nestorian Church): in schism since 431 AD (Nestorian Schism), eventually separated into two distinct bodies: the Assyrian Church of the East (in schism) and the Chaldean Catholic Church (in full communion).
Chaldean Church traces its roots to St. Thomas
Holy Apostolic Catholic Assyrian Church of the East (aka Assyrian Church of the East): schismatic since 431 AD
Chaldean Catholic Church: in full communion with Rome, under the Chaldean Catholic Patriarch of Babylon Louis Raphaël I Sako
The Syriac Church of Antioch traces its roots to St. Peter.
Syriac Orthodox Church: in schism since 451 AD.
Syriac Catholic Church: in full communion with Rome, under the Patriarch of Antioch and all the East of the Syrians Ignatius Joseph III Yonan
“Roman Catholic Church” is a generic name for the Church of Jesus Christ. The one Church of Christ has been universally recognized as bearing the four marks: One, Holy, Catholic, Apostolic. After the first schisms began to occur, a gradual development led to a universal acceptance that the Church is also Roman inasmuch as the See of Rome (known as the Apostolic See or Holy See) is the See of the successor of Peter, the Vicar of Christ, whom is the visible head of the Church. The term “Roman Catholic Church” thus describes the One Church of Christ, which is composed of 23 sui iuris “rites” or “churches”, the largest of which is the Latin Church. More here. The Latin Church itself generally traces its roots in Rome to the blessed apostles Peter and Paul, the former having been the first bishop and pope, dying a martyr on Vatican Hill, where the Basilica of St. Peter currently stands.
Orthodox Catholic Church: in schism since 1054 AD. This is actually composed of several self-governing (autocephalous) ecclesial bodies (a list here).
The Saint Thomas Christians, also called Syrian Christians or Nasrani, are an ancient community of Semitic Christians from Kerala, India who trace their origins to the evangelistic activity of Thomas the Apostle. Historically the Saint Thomas Christian community was part of the Church of the East. The Saint Thomas Christians are now divided into several different Eastern Catholic, Oriental Orthodox, and independent bodies. The following are in full communion with the Holy See:
- Syro-Malabar Catholic Church, headed by the Major Archbishop of Ernakulam-Angamaly, Cardinal Mar George Alencherry
- Syro-Malankara Catholic Church, headed by the Major Archbishop Moran Mor Baselios Cardinal Cleemis Catholicos.