This is a mix of Celtic and Gardenarian beliefs. These traditionals move mostly within the Farrar studies and are fairly structured in their beliefs. They train through a degree structured process. The International Red Garters is the most famous organization at this time. Often includes druids.
The term “British Traditional” refers to a variety of traditions which originated in the British Isles and which have certain characteristics in common. There is a mix of Celtic and Gardnerian beliefs, mostly based on the Farrar stuies. Worship of the God and Goddes is balanced, covens and co-ed, and there is a degree system. The New Wiccan Church is a federation of British Traditions (Gardnerian, Slexandrian, Mohisian, and Central Valley Wicca-Kingstone, majestic Order and Silver Crescent). NWC is dedicated to preserving initiatorty Craft.
British Traditional Wicca, or BTW, is an all-purpose category used to describe some of the New Forest traditions of Wicca. Gardnerian and Alexandrian are the two best-known, but there are some smaller subgroups as well. The term “British Traditional Wicca” seems to be used in this manner more in the United States than in England. In Britain, the BTW label is sometimes used to apply to traditions which claim to predate Gerald Gardner and the New Forest covens.
Although only a few Wiccan traditions fall under the “official” heading of BTW, there are many offshoot groups which can certainly claim kinship with the British Traditional Wiccans. Typically, these are groups which have broken off from a BTW initiatory line, and formed new traditions and practices of their own, while still being loosely connected with BTW.
One can only claim to be part of British Traditional Wicca if they (a) are formally initiated, by a lineaged member, into one of the groups that falls under the BTW heading, and (b) maintain a level of training and practice that is consistent with the BTW standards. In other words, much like the Gardnerian tradition, you can’t simply proclaim yourself to be British Trad Wiccan.
Geography doesn’t necessarily determine whether or not someone is part of BTW. There are branches of BTW covens located in the United States and other countries — again, the key is the lineage, teachings and practice of the group, not the location.