Paganism is an umbrella term that covers a wide variety of religions that are based on old religions not Christian, Jewish, or Muslim in origin. Most Pagans believe in the existence of many different Gods and Goddesses, see Nature as sacred, and often hold to the concept of reincarnation.
Wicca is a very specific religion (Also considered to be Pagan) which is based on the pre-Christian religions of northern Europe. But Wicca is a modern religion largely created by Gerald Gardner in the 1940's. If you look through the stuck threads in the Wicca Forum you'll find a lot of information about Wiccan beliefs. Wiccans worship both a Horned God and a Goddess of the Moon. Wiccans do practice witchcraft as part of their religion.
Witchcraft is simply a form of magical practice which has no specific ties to any religion. One could be an Asatru, a Buddhist, a Christian, a Muslim, a Wiccan, or a Zoroastrian and still practice witchcraft.
There are some Witches who also view witchcraft (the magical practice) as being part of their version of a Pagan religion. These Witches are NOT Wiccan and have their own specific beliefs and practices. Therefore it would be possible to say that all Wiccans are Witches, but not all Witches are Wiccan.