Trinitarian Wicca is the correct name of the tradition often generalized into a practice called Christian Wicca. Trinitarian Wicca is a tradition based on American Wicca, boasting no direct lineage. Trinitarians work exclusively with the Goddess-inclusive Christian Pantheon. This tradition is not eclectic nor is it ChristoPagan because our devotion lies exclusively with the Christian pantheon. Trinitarian practitioners celebrate the Wiccan Way, observing the 8 Sabbats, the 13 Esbats, and upholding the Wiccan Rede.
For the Trinitarian path, there are no trappings of Patriarchal Christianity. We do not have conflicts with the Bible, because we work directly with the Gods and Goddesses; church dogma does not have a place in our ritual structure. Concepts such as the original sin, salvation, baptism, heaven, hell, and Satan are not conflicting topics for Trinitarians. They have no place in Wicca at all; as Trinitarian Wiccans, we do not differ in this belief. There is nothing fundamental about Christian or Trinitarian Wicca.
As for Christian Wicca, the term Christian is used as a modifier for the pantheon observed in this particular practice of Wicca, much like the concept of Celtic Wicca. Starting in October of 1999, Christian Wicca began on Yahoo Groups as a working title reflecting the an eclectic practice of American Tradition of Wicca. By 2002, this path developed it's name, the Trinitarian Tradition. This tradition evolved as a group of Wiccan practitioners focused on a Goddess-inclusive Christian trinity.
The mere term Christian Wicca upset so many people both Christian and Wiccan, that it actually got in the way of the true meaning of the path. That was never our intent. While the term Christian Wicca was more descriptive, Trinitarian Wicca is far more accurate and far less controversial. However, by the time the book came out - the working term had become popular and it was hard to express the concepts of Trinitarian Wicca without using the term Christian in the definition.