Where 'Alexandrian' Came From
The Alexandrian Tradition got its name from a play on words that Stewart Farrar coined. The name does not refer to 'AlexSandrian' with reference to its founder, Alex Sanders, but rather refers to the Library at Alexandria, which has been heralded as the pinnacle of enlightenment in the Ancient World. One of the hallmarks of the Library of Alexandria was that it included knowledge from a broad number of sources, and therefore it was seen as more 'inclusive' and accepting of the various sources of wisdom. The Librarians were also guardians of many of the Mysteries of the ancient Egyptians, many of which included texts and codices of metaphysics, alchemy, and other occult and esoteric teachings which are today viewed as magic.
The destruction of the Library of Alexandria was one of the greatest crimes against the development of humankind yet. It is because of this destruction that we retain only partial and fragmentary memories of the lore and wisdom of ages past. It is also because of this monumental loss that a knowledge base which previously was relatively widely accessible (to most people) and publicly known became scarce, and in its scarcity became esoteric, and more hidden, literally 'occult'.
This heritage is part of what Stewart Farrar was alluding to by coining the term 'Alexandrian'. One of the defining traits of the Alexandrian Tradition as different from the other lines of British Traditional Wicca is that Alex Sanders worked very hard to blend the peasant religion of the Wicca with the practices of High Magic. Although Gerald Gardner also borrowed heavily on High Magical sources to help fill in what he perceived were gaps in the lore and rituals of the Wicca, Alex Sanders took it a step further and integrated certain elements of the philosophy and metaphysical dogma concerning non-Judeo-Christian High Magic.
As time passed, however, this integration became more and more of an elective branch of the Alexandrian lore, to be studied in-depth by those so motivated by their own magical development. The High Magic lore is present for any coven to use to broaden their magical practices and development, while the original religious lore of the Wicca is also perfectly preserved to allow those who wish to focus solely on the 'low' magical aspects to do so. Since the revival of Wicca is a conglomerate set of lore and rituals to begin with, it's impossible to neatly divide things between High- and Low Magic, but the terms are used as a point of reference.
Variations Between the Covens And Downlines
Because there is so much lore and material which Alex Sanders developed in his pursuit of deeper meaning and the integration of High Magical practices into the rites and lore of the Wicca, Alexandrian coven leaders find themselves presented with many different ways to practice, all of which fall within the broad definition of 'Alexandrian'. This is common to a lesser extent within all of the Traditions of the Wicca, but more so in the Alexandrian Tradition because of all the additional material authored and compiled by Alex.
The lore and rituals of the Initiations and Elevations are practiced according to the original methods used by the revivalist Wiccans, however. This provides a common denominator which links together all of the Alexandrian covens and the rest of the Wiccan Traditions as a whole. Because of the amount of variation which can possibly be found among the Alexandrian downlines, it is usual to find a greater degree of tolerance and respect for variation among Alexandrians than it is with some of the other, more inflexible Traditions of the Wicca. This is all with the proviso, however, that certain core aspects need to be maintained, and certain practices that define the Tradition as a Tradition need to be maintained.
The Alexandrian Tradition tends to experience such variety that blanket statements can be very misleading. As one Elder of the Alexandrian Craft put it, "There are stranger cults than ours, and some of them are Alexandrian."