James, my friend,
Ahh, you do ask tough questions at times
I'll give a very brief explanation here and then I recommend the explanation offered in the first few posts to this stickied thread
as a starting point.
Old Believers or Old Ritualists were originally Russian Orthodox faithful who were distressed by the actions of Patriarch Nikon of Moscow in the mid-17th century. The Patriarch was convinced that the Church needed to return to an older, more correct praxis in both its spirituality and liturgical expression.
To achieve this, he felt that it needed to go back to Greek texts as he perceived that subsequent mistranslations of them had led to errors. Nikon's 'reforms' (many of them enumerated in one of the posts at the above link) were controversial and had far-reaching consequences - many of those opposed believing that the reforms presaged the appearance of the Anti-Christ or even that Nikon himself or the Tsar, who supported him, were either the Anti-Christ's agents or the Anti-Christ.
Those who rejected the reforms were termed Raskols or Raskolniks and deemed to be schismatic, if not worse, and persecutions on a horrific level resulted. The Old Believers or Old Ritualists eventually came to be divided into two main types - Popovotsy or priested and Bespopovotsy or priestless (a third, the Begolopopovtsy, sometimes priested, represented a small minority).
Many of the Bespopovotsy didn't start out that way but as their priests died out they lacked hierarchs to ordain replacements and gradually found themselves having to discover how to live their spiritual life absent a priesthood. Others were unable to find priests sympathetic to their cause and had to do likewise. Still others rejected an earthly priesthood as being superfluous in what they perceived as what we would term 'End Times'.
These divisions still exist, although the more eccentric of the Bespopovotsy concords/agreements (terms applied to the sects) have become extinct, as have virtually all of the more extreme offshoots that arose contemporaneously with the Old Believers/Old Ritualists and were often erroneously identified with them.
There is a set of 5 stickied threads at the top of this subforum which enumerate, in varying levels of detail, some of the 100s of sects which arose in that era.
We have a few members here who are of the Popovotsy and did have at least one, although he hasn't posted for a long while, who was of a Bespopovotsy sect.
My friend and brother, Tom/Polish American, whose threads and posts dominate this subforum is not an Old Believer/Old Ritualist, but has a very strong interest in them, is an incredible resource on the topic, and maintains contact with several of the sects - priested and priestless - in the US. Myself and a few others here are also very interested in the subject.
There is a small community in Russia of Catholic Old Ritualists (priested, obviously). They are the remnant of a larger community within the Russian Greek-Catholic Church in pre-Revolutionary times. There was, briefly, another such community in Oregon, but its members were ultimately subsumed into the priested Orthodox community for lack of a Catholic presbyter to serve them. Very recently, in the Prayer Forum, we mourned Brother Ambrose Moorman, OSB, of blessed memory, a Benedictine monk who was of the Old Rite and the last Catholic Old Ritualist in the US.
Old Believers/Old Ritualists in North America are found mainly in PA, OR, WA, and AK in the US and in the western Canadian provinces of BC, AB, SK, MB. (Small communities can also be found in northern CA, several US border states from MI westward, and likely in the Canadian territories of NU and NT.)
There are also commmunities in Brazil and Australia, in many East European countries, and in Turkey and Armenia.