Wicca is a modern religion based upon the earlier, pre-Christian practices of Western Europe. What we know of as Wicca today is largely a synthesis of practices brought to public attention by Gerald Gardner and Doreen Valiente in 1954.
The practice of Wicca also includes the magical practice of witchcraft, so essentially all Wiccans are Witches. However, it is important to remember that there are also Witches who do not ascribe to the beliefs of Wicca...so it is correct as well to say that not all Witches are Wiccans.
If you'd like to learn more about what Wiccans believe there is an excellent site at http://wicca.cnbeyer.com/wicca101/index.shtml
Neither Wiccans nor Witches are the only ones who can cast spells. Certainly one does not have to become Wiccan and adopt the religion in order to be a spellcaster.