If you don't have personal experience, it's difficult to tease out the difference between Wiccans and witches. Part of the issue is that many practitioners of Wicca religion consider the terms interchangeable. While either term may be appropriate, our classic ideas of witches don't apply to Wiccans, although practitioners of the past may have been among those persecuted in witch trials.
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Wicca is the largest Neopagan religion but is very broadly defined. It is a decentralized religion with no fundamental rituals, books, or beliefs beyond a deep reverence for the Earth and the commitment to do no harm. Many Wiccans practice their religion as individuals, although some do form covens. Stories of witches and witchcraft have been around longer than we can truly know but the Wiccan religion seems to date back to only the 19th century or so. This means that, while some of the victims of witch hunts and burnings may have practiced precursors to Wicca, many did not.
Snapping to judgment is an unfortunate tendency of human nature; one that is particularly potent when we feel we've identified people who differ from ourselves. The idea of Wicca, because it is not a major world religion and is related to (or possibly the same as) witchcraft, can scare us. But it can also be traced back to belief systems with which we are more comfortable, like Ancient Egyptian, Greek, and Norse religions - all considered Pagan. Still uneasy? Well then you might have to reevaluate your thoughts about Christmas, Halloween, and Groundhog Day because these cultural celebrations all have Pagan roots too.
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Read more about Wicca:
ReligiousTolerance.org: Wicca: a Neopagan, Earth-centered religion
The Church and School of Wicca: A Definition of Wicca