Although there are a lot of churches called 'Orthodox', there are really only two groups normally called 'Orthodox'. The usual terms are 'Eastern Orthodox' and 'Oriental Orthodox'. Since eastern and oriental are synonyms, it
is confusing. For those who know Christian history, the Eastern Orthodox are Chalcedonian Christians, the Oriental Orthodox are Non-Chalcedonians.
The
Eastern Orthodox (officially Orthodox Catholic Church) is far more numerous (it is the second largest body of Christians) and includes most of the churches Westerners have heard of at one time: the various 'Greek Orthodox' with their centres in Jerusalem, Alexandria, Antioch, Constantinople (Istanbul), Cyprus, Mount Sinai, and Athens; the Russian Orthodox Church, the Orthodox Church in Japan, the Serbian Orthodox Church, the Bulgarian Orthodox Church, the Romanian Orthodox Church, the Georgian Orthodox Church, the Orthodox Church of Albania, the Orthodox Church in America, the Polish Orthodox Church, the Orthodox Church of the Czech Lands and Slovakia.
The Non-Chalcedonian Oriental Orthodox church which is probably most-familiar to Westerners is the Coptic Church in Egypt.
The
litya is common to all the Chalcedonian Orthodox. If the Oriental Orthodox have it (and I strongly suspect they do), they would have a different name for it.