There are so many different traditions and branches, that I doubt anyone could come close to defining them all. The following are the more...known branches.
Gardnerian
A closed initiary Tradition founded in England circa 1953 by Gerald Gardner, and further developed by Doreen Valiente. Gardner gave his Tradition a ritual framework influenced strongly by Freemasonry and Crowley-an magic, as well as traditional folk magic and Tantic Hinduism. In 1965 this Tradition was brought to the USA by Raymond and Rosemary Buckland, who were initiated in 1964.Gardnerian covens are headed by a High Priestess and have 3 degrees of initiation, which closely parallel the Masonic degrees. Worship is centered on the Goddess and Horned God. The Wiccan Rede is this Traditions guiding principal, and eight seasonal Sabbats are observed. Power is raised through scourging and sex magick, as well as meditation, chanting, dancing, wine and cords. Covens work skyclad. Though designed for coven/group work, solitary workings have been created.
Alexandrian
Founded in England during the 1960's by Alexander Sanders,self-proclaimed "King of the Witches". An offshoot of Gardnerian,Alexandrian covens focus strongly upon training, emphasizing on areas more generally associated with ceremonial magic, such as Qabalah, Angelic Magic and Enochian. The typical Alexandrian coven has a hierarchical structure, and generally meets on weekly, or at least on Full Moons, New Moons and Sabbats. Rituals are usually done skyclad.Most Alexandrian covens will allow non-initiates to attend circles, usually as a "neophyte," who undergoes basic training in circle craft prior to being accepted for the 1st degree initiation. Alexandrian Wicca uses essentially the same tools and rituals as Gardnerian Wicca, though in some cases, the tools are used differently, and the rituals have been adapted. Another frequent change is to be found in the names of deities and guardians of the Quarters. In some ways these differences are merely cosmetic, but in others, there are fundamental differences in philosophy. Over the last 30 years, the two traditions have moved slowly towards each other, and the differences which marked lines of demarcation are slowly fading away.
British
British Traditionals are, generally, any of the old traditions the originated on the British Isles: Gardnerian, Traditional Celtic, Alexandrian, New Forest..etc. *Thanks again to Aldwyn for the info.*Celtic
Traditional Celtic Wicca- I don't know much about this tradition, but would like to point out that it is different from the "general" Celtic heading. The Traditional Celtic Wicca tradition can be traced back in modern times to a contemporary of Gerald Gradner. Her name was Lady Circe, and all TCW can trace their lineage back to her, just as all Gardnerians can trace their lineage back to Gerald Gardner. Thanks Aldwyn for the info!!The Celtic path is really many traditions under the general heading of "Celtic." It encompasses Druidism, Celtic Shamanism, Witta, the Grail Religion,and Celtic Christianity or Culdees. Each path is unique and stand alone, but they meld together with another and can still be part of the Celtic heading. These are primarily derived from the ancient pre Christian Celtic religion of Gaul and the British Isles. As it is practiced today, most of the Celtic paths are part of the Neo-Pagan revival, focusing on Nature and healing with group and individual rituals that honor the Ancient Shining Ones and the Earth. Most are very eclectic, and hold to the Celtic myths, divinities, magic and rituals. Celtic paths are some of the more popular traditions.
Ceremonial Witchcraft
Followers of this Tradition use a great deal of ceremonial magic in their practices. Detailed rituals with and Egyptian flavor are sometime a favorite, or they may use the Cabalistic magic.Dianic
This is the most feminist Craft Tradition. Most Dianic covens worship the Goddess exclusively (Diana and Artemis are the most common manifestations) and most today are women only. Rituals are eclectic; some are derived from Gardnerian and Faery traditions, while others have been created anew. Emphasis is on rediscovering and reclaiming female power and divinity, consciousness-raising, and combining politics with spirituality.The Dianic Craft includes two distinct branches:
The first Dianic coven in the U.S. was formed in the late '60s by Margan McFarland and Mark Roberts, in Dallas, Texas. This branch gives primacy to the Goddess in its theology, but honors the Horned God as Her beloved Consort. Covens include both women and men. This branch is sometimes called 'Old Dianic,' and there are still covens of this tradition specially in Texas. Other covens, similar in theology but not directly descended from the McFarland/Roberts line are sprinkled around the country.
The other branch, Feminist Dianic Witchcraft, focuses exclusively on the Goddess and consists of women-only covens, often with a strong lesbian presence. These tend to be loosely structured and non-hierarchal, using consensus decision making and simple, creative, experimental ritual. They are politically feminist groups, usually very supportive, personal and emotionally intimate. The major network is Re-Formed Congregation of the Goddess. Z Budapest founded the Susan B. Anthony Coven in 1971, declaring Dianic Witchcraft to be "Wimmin's Religion". The Wommin's Spirituality Forum was Founded by Z Budapest in 1986, and is dedicated to bringing Goddess consciousness to the mainstream of feminist consciousness through lectures and, retreats, classes, cable TV shows, and rituals in the effort to achieve spiritual and social liberation.
Eclectic
The term Eclectic refers to groups and individuals not following any one particular Tradition or mythos. Rather they incorporate elements of several, according to the training, preferences and experiences of the practitioners. Deities from several pantheons may be invoked, sometimes even in the same ritual, particularly when a working is being created for a specific cause. In such a case, Eclectics may call upon, for example, an assortment of Love Goddesses, etc. from many different cultures.Solitary
A Solitary Witch is just that- they practice alone, regardless of tradition, denomination, or sect. Some were initiated into a coven and eventually chose to extricate themselves and practice that particular Tradition or sect by themselves. A Solitary Witch can also be an individual who has no desire to practice with or learn from a coven structure, but may still adhere to a specific Tradition thru the teachings of another. Finally, a Solitary Witch can be a person who has decided to tough it out on their own, learning from books, networking, and fellow Witches of different Traditions. More and More people are selecting the solitary path rather than that of group interaction.Faery, Faerie, Fairy, Feri
It is an ecstatic, rather than fertility tradition, emphasizing on polytheism, practical magic, self-development and theurgy. Strong emphasis is placed on sensual experience and awareness, including sexual mysticism, which is not limited to heterosexual expression. This is a mystery tradition of power, mystery, danger, ecstasy, and direct communication with divinity. Most initiates are in the arts and incorporate their own poetry, music and invocations into rituals.The Tradition is gender-equal, and all sexual orientations seem able to find a niche. According to Francesca De Grandis, founder of the 3rd Road branch: "Faerie power is not about a liturgy but about one's body: a Fey shaman's blood and bones are made of stars and Faerie dust. A legitimate branch of Faerie is about a personal vision that is the Fey Folks' gift to a shaman." Initially small and secretive, many of the fundamentals of the Tradition have reached a large audience trough the writings of Starhawk, the most famous initiate. Some secret branches remain. While only a few hundred initiates can trace their lineage directly to Victor Anderson, many thousands are estimated to practice neo-Faery Traditions.