Witchcraft is a practice and a system. There are some beliefs tied to it, but they are not required. There is a huge difference between western Witchcraft and anthropological Witchcraft.
Wicca is a tricky one, because when Wicca really started to become popularized (around 1940. Actual inception dates vary, but most agree it began in the early 20th century), it meant something very specific: a lineaged, initiatory priesthood of the Old Religion incorporating Witchcraft and mysticism in the Rites. At that time, there was none of this “I’m Wiccan but not a witch” stuff. Again, it was a practice. Though there were beliefs tied to it, they were not required. The oft touted “Wiccan rede” was not a part of original Garderian Wicca; it came from another line of initiatory Witchcraft (NECTW).
Over time, and particularly in the last 20 years or so, the word “Wicca” has become remarkably diluted. Now just about anyone with pagan beliefs who likes to put colored candles at the corners of a circle calls themselves “Wiccan”. Popular books have put forth the idea that Wicca isn’t about Witchcraft at all (although I would argue that it is nearly impossible to properly perform Wiccan ritual without a strong working knowledge of Witchcraft.) and that it is merely a “belief system”.
I wrote an essay several years ago on what it means to hold on to the traditional way of thinking versus the popular “eclectic wicca” view. If you are really interested, it is available here.