ACS could not really be called a Alexandrian Coven. Although it's core ritual components were based upon a 'Alexandrian' tradition. Therefore ACS is rather unique.
Witchcraft, Wicca and Ceremonial Magick are similar yet different practices related by a common ancestor, lost in history. Shamanism may be the closest relative of each-as I have indicated below however, no one can really be sure. It is because of their similarity that Ceremonial Magick, Wicca and Witchcraft are innocently confused with each other. Most people like to attach themselves to a particular path or tradition, just as I have labeled myself a Celtic-Alexandrian Wicca. Others may label themselves as 'Dianic', 'Eclectic', 'Ceremonial Magician of the New-Reformed Ancient Order of the Purple...'. Well, you get it! Anyhow, I have created the chart below, showing how some traditions are similar to others and where they differ. I have omitted several traditions that may be considered 'Pagan' such as Voudon, Druidism, etc. Mostly because those traditions are not as commonly confused with each other as these three.
Note: Regarding the chart above. The beginning and end to each 'time-line' is approximate. Also I did not include other cultures and kept the chart focused on Indo-European history of Western traditional magic(k).
Witchcraft in the Western Tradition, is either believed to be a hereditary-line of people who were called 'Witches' by the Inqusition during the 15th through 18th centuries, but escaped persecution. Or, claim to have a family tradition that can be traced back before or during that period. The romantic notion that such a tradition has been preserved and continues through a family line for all these centuries is inviting and may well be true. I have no proof of this, I can not argue for or against this theory. Most people who like to distinguish themselves as 'Witches' instead of 'Wiccan' fall into this catagory and may call their family tradition "The Craft", "Wise-women", "The Wise", "Crafters", "Wise-Craft", etc.
Witches or people who were accused of practicing witchcraft were supposedly capable of causing injury to cattle, killing people (especially kings) with wax images, they could raise winds and storms -often selling 'witches ladders' to sailors who would unravel one of the consecutive knots tied in a rope to raise a wind when needed. They transformed men into beasts -of course that isn't to difficult...lol, and caused impotence -Yikes, is that really her fault?!. Mid-wifes accused of witchcraft were said to drink the blood and eat the flesh of unborn children.
The Witch craze during the
15th through 18th centuries sometimes reffered to as the 'Burning
Times' is still to this day very misunderstood. Most people
believe that the accusation of witchcraft was used as an excuse
to eliminate and/or silence political opponents or women of power,
and that is a reasonable theory and I agree, to a certain extent.
For reference; during 319 -
321 AD several laws were introduced (through the Roman Catholic
Church) to penalize and punish practioners of the craft of divination
and haruspex (a form of divination).
"Desiring with the most heartfelt anxiety, even as Our Apostleship requires, that the Catholic Faith should especially in this Our day increase and flourish everywhere, and that all heretical depravity should be driven far from the frontiers and bournes of the faithful..."
-Malleus Maleficarum. 1484 CE
Translation: Drive away (by what means?) all heretics because they threaten the Christian faith. Who are these heretics? Simple, any person or persons who holds controversial opinions, especially one who publicly dissents from the officially accepted dogma of the Roman Catholic Church.
Between the 15th and 18th centuries; some 300,00 to 600,000 people were accused of heresy and put to death. This number does not include all the people who were also accused of heresy and put to death since 317 AD. Many of these so called 'heretics' were Jews, Muslums, Mid-wifes, Herbalists/Healers, Diviners, Pagans, and Witches (whether they called themselves this or not - is not known). The last trial of Witchcraft was Anna Goeldi who was hanged at Glaris, Switzerland June 17, 1782. Also, many accused of Witchcraft were hung and not burned at the stake.
Back in medieval times if you called your self a 'witch' it was a death sentence. Whether you believed in the Roman Catholic Church or not, you acted like it. You went to Church and you prayed and spoke like a good Catholic.
The spread of propaganda continues to this day. Special note: From the Old Testament Bible in Exodus 22:18 reads: "Thou shalt not suffer a witch (sorceress) to live.", is a mistranslation from the Hebrew "Thou shalt not suffer a poisoner (of wells/water) to live." From Latin the term for sorceress is venefica which is also the term for a poisoner.
The history of Wicca is really quite interesting and very convoluted. The Witche's craft that Gardner was initiated into and Alexander Sanders spread out among the many he initiated is a construction of several philosophies. The occult material; alchemy, Caballa, Masonic and Medieval magic. The main source of material is said to be the Lesser Key of Soloman. With additional material from Eliphas Levi's books and Crowley. I am briefly outlining the material because I do not want to analyze the material as much as I do the source of the material. Wicca, therefore maybe based on an ancient practice or a reconstruction of an ancient practice.
Either way, to over simplify. The terms "Witchcraft or Wicca" etymological speaking are the same word. The word we use today for 'Witch' is derived from the Saxon word 'wicca' which is a masculine noun, pronounced 'witch-ah', the feminine noun is spelled 'wicce' and is pronounced 'witch-eh'. The plural form is 'wiccan' (m) and 'wiccen' (f). The commonly used term 'wiccan' is pronounced 'witch-in'. Now, the common usage of these terms differs today. A practitioner who calls themselves 'wiccan' most likely practices a reconstruction of an ancient practice of witchcraft. Most of the time they will associate themselves with either Gardnerian or Alexandrian traditions.
Most of the Medieval 'grimoires' I have read are full of Medieval superstition. Later development of the material by the Golden Dawn is very symbolic and deep. Every grade of the GD is a stepping stone of symbolic and psychological material that prepares the student for the next grade. Trying to understand the advanced material without having anunderstanding of the basic material, will be fruitless. Hebrew lettering is not used in our tradition because it is void of meaning if used. To us (ACS) writing names in Hebrew has as much meaning as writing them in Chinese or Arabic. Those ancient names of power seen within some magic circles are just English words for Hebrew names of God, again useful to the Cabalist, not useful to our tradition of Wicca. The subject of Caballah is also out of this websites scope to explain, I have read and can relate to much of Cabalistic magick but, it is a path unto itself and I could not begin to illuminate it.
We do not invoke names or write names we do not understand. Medieval magicians would create circles for holding demonic spirits and for protecting themselves from possible retaliation from said spirits, and would use iron (the sword) and salt and quotes from the bible to protect themselves. Finding and pronouncing the names of spirits acurately was also very important to gaining power over the spirit in question. To us invoking a name without understanding or having history behind it, is void of meaning.