Although all Old Believers groups emerged as a result of opposition to the Nikonian reform, they do not constitute a single monolithic body. In fact, the Old Believers feature a great diversity of groups that profess different interpretations of the church tradition and often are not in communion with each other. Some groups even practice re-baptism before admitting a member of another group into their midst.
The terminology used for the divisions within the Old-Believer denomination does not always make precise delineations. Generally, people may refer to a larger movement or group — especially in the case of such major ones as popovtsy and bespopovtsy — as a soglasie or soglas (in English: "agreement" or more generally, "confession"). Another term, tolk (English: "teaching") usually applies to lesser divisions within the major "confessions". In particular it can characterize multiple sects that have appeared within the bespopovtsy movement.
Popovtsy
Since none of the bishops joined the Old Believers (except Bishop Pavel of Kolomna, who suffered execution), apostolically ordained priests of the old rite would have soon become extinct. Two responses appeared to this dilemma: the “priestist” Old Believers (поповцы (Popovtsy)) and the non-priestist Old Believers (беспоповцы (Bespopovtsy — literally "priestless ones")).
The Popovtsy represented the more moderate conservative opposition, those who strove to continue religious and church life as it had existed before the reforms of Nikon. They recognized ordained priests from the new-style Russian Orthodox church who joined the Old Believers and who had denounced the Nikonian reforms. In 1846 they convinced Amvrosii Popovich (1791-1863), a deposed Greek Orthodox bishop whom Turkish pressure had had removed from his see at Sarajevo, to become an Old Believer and to consecrate three Russian Old-Believer priests as bishops. In 1859, the number of Old-Believer bishops in Russia reached ten, and they established their own episcopate, the Belokrinitskaya hierarchy. Not all priestist Old Believers recognized this hierarchy. Dissenters known as беглопоповцы (beglopopovtsy) obtained their own hierarchy in the 1920s. The priestist Old Believers thus manifest as two churches which share the same beliefs, but which treat each other's hierarchy as illegitimate. Popovtsy have priests, bishops and all sacraments, including the eucharist.
Belokrinitskaya hierarchy - The largest Popovtsy denomination. One can refer to the Russian part of this denomination as the Belokrinitskoe Soglasie (the "Belokrinitsky Agreement") or as the Russian Orthodox Old-Rite Church.
Okruzhniki (extinct)
Neokruzhniki (extinct)
Novozybkovskaya hierarchy or Russian Old-Orthodox Church
Beglopopovtsy (extinct, now the Russian Old-Orthodox Church)
Luzhkane, also known as Luzhkovskoe soglasie (extinct). In some places, they had no priests and so belonged to Bespopovtsy.
Bespopovtsy
The Bespopovtsy (the "priestless") rejected "the World" where Antichrist reigned; they preached the imminent end of the world, asceticism, adherence to the old rituals and the old faith. The Bespopovtsy claimed that the true church of Christ had ceased to exist on Earth, and they therefore renounced priests and all sacraments except baptism. The Bespopovtsy movement has many sub-groups. Bespopovtsy have no priests and no eucharist.
Pomortsy or Danilovtsy (not to be confused with Pomors) originated in North European Russia (Russian Karelia, Arkhangelsk region). Initially they rejected marriage and prayer for the Tsar.
Novopomortsy, or "New Pomortsy" - accept marriage
Staropomortsy, or "Old Pomortsy" - reject marriage
Fedoseevtsy – “Society of Christian Old Believers of the Old Pomortsy Unmarried Confession” (1690s- present); deny marriage and practise cloister-style asceticism.
Fillipovtsy.
Chasovennye (from a word chasovnya - a chapel) - Siberian branch. The Chasovennye initially had priests, but later decided to change to a priestless practice. Also known as Semeyskie (in the lands east of Baykal Lake).
Bespopovsty: Minor groups
Aside from these major groups, many smaller groups have emerged and died out at various times since the end of 17th century:
Aristovtsy (beginning of 19th to the beginning of 20th centuries; extinct) - from the name of the merchant Aristov;
Titlovtsy (extinct in 20th cent.) - emerged from Fedoseevtsy, supported the use of Pilate's inscription upon the cross (titlo), which other groups rejected;
Troparion confession (troparschiki) - a group that commemorated the tsar in the hymns (troparia);
Daniel’s confession of the “partially married” (danilovtsy polubrachnye);
Adamant confession (adamantovy) - refused to use money and passports (as containing the seal of Antichrist);
Aaron's confession (aaronovtsy) - second half of the 18th century, a spin-off of the Fillipovtsy.
“Grandmother’s confession” or the Self-baptized - practiced self-baptism or the baptism by midwives (babushki), since the priesthood — in their opinion — had ceased to exist;
“Hole-worshippers” (dyrniki) - relinquished the use of icons and prayed to the east through a hole in the wall (!);
Melchisedecs (in Moscow and in Bashkortostan) - practiced a peculiar lay "quasi-eucharistic" rite;
“Runaways” (beguny) or “Wanderers” (stranniki);
“Netovtsy” or Saviour’s confession - denied the possibility of celebrating sacraments and praying in churches; the name comes from the Russian net "no", since they have "no" sacraments, "no" churches, "no" priests etc.
Edinovertsy
Edinovertsy (Russian: единоверцы -- 'people of the same faith', as opposed to староверы -- people of the "old faith", i.e., Old Believers) - Agreed to become a part of the official Russian Orthodox Church while saving the old rites. First appearing in 1800, the Edinovertsy come under the omophorion of the Russian Orthodox Church of the Moscow Patriarchate or of the Russian Church Abroad. They retain the use of the pre-Nikonian rituals.
Validity of the Reformist Theory: sources of Russian traditions
Vladimir officially converted the Eastern Slavs to Christianity in 988, and the people had adopted Greek Orthodox liturgical practices. At the end of 11th century, the efforts of St. Theodosius of the Caves in Kiev (Феодосий Киево-Печерский, d. 1074) introduced the Studite Typikon to Russia. This typikon reflected the traditions of the urban monastic community of the famous Studion Monastery in Constantinople. The Studite Typikon predominated throughout the western part of the Byzantine Empire and was accepted throughout the Russian lands. In the end of 14th century, through the work of St. Cyprian, metropolitan of Moscow and Kiev, the Studite liturgical practices were gradually replaced in Russia with the Jerusalem Typicon or the Typicon of St. Sabbas - originally, an adaptation of the Studite liturgy to the customs of Palestinian monasteries. The process of gradual change of typica would continue throughout the 15th century and, because of its slow implementation, met with little resistance - unlike Nikon's reforms, conducted with abruptness and violence. However, in the course of 15th-17th centuries, Russian scribes continued to insert some Studite material into the general shape of Jerusalem Typicon. This explains the differences between the modern version of the Typicon, used by the Russian Orthodox Church, and the pre-Nikonian Russian recension of Jerusalem Typicon, called Oko Tserkovnoe (Rus. "eye of the church"). This pre-Nikonian version, based on the Moscow printed editions of 1610, 1633 and 1641, continues to be used by modern Old Believers.
However, in the course of the polemics against Old Believers, the official Russian Orthodox Church often claimed the discrepancies (which emerged in the texts between the Russian and the Greek churches) as Russian innovations, errors, or arbitrary translations. This charge of "Russian innovation" re-appeared repeatedly in the textbooks and anti-raskol treatises and catecheses, including, for example, those by Dimitri of Rostov. The critical evaluation of the sources and of the essence of Nikonian reforms began only in the 1850s with the groundbreaking work of Nikolai F. Kapterev (1847-1917), continued later by Serge Zenkovsky. Kapterev demonstrated—for the first time to the wider Russian audience—that the rites, rejected and condemned by the Nikonian reforms, were genuine customs of the Orthodox Church which suffered alterations in the Greek usage during the 15th-16th centuries, but remained unchanged in Russia. The pre-Nikonian liturgical practices, including some elements of the Russian typicon, Oko Tserkovnoe, were demonstrated to have preserved many earlier Byzantine material, being actually closer to the earlier Byzantine texts than some later Greek customs (Kapterev, N.F. 1913; Zenkovsky, S.A. 2006).
Remarkably, the scholars who opened the new avenues for re-evaluation of the reform by the Russian Church — Kapterev and E.E. Golubinsky — themselves held membership of the "official" church, but took up study of the causes and background of the reforms and of the resulting schism. Their research revealed the official theory regarding the old Russian books and rites as unsustainable. Zenkovsky has described Kapterev's as [...] the first historian who questioned the theory about the “pervertedness” or incorrectness of the Old Russian ritual and pointed out that the Russian ritual was not at all perverted, but had on the contrary preserved a number of early Old Byzantine rituals, among them the sign of the cross with two fingers, which had been changed later on by the Greeks themselves, in the 12th and 13th century, which caused the discrepancy between the Old Russian and the New Greek church rituals. — Zenkovsky, S.A., Russkoe staroobrjadčestvo, 1970,1990, p. 19-20.
http://www.orthodoxwiki.org/Old_Believers