Sorry, I'll stick my nose in here. All Wiccans are Witches as well (Though as Brysing said, not all Witches are Wiccan). Many Wiccans do not cast spells or do it very seldom, but we use magic all the time. If you're not using magic to cast a circle, consecrate tools, etc then you are not a Wiccan.
But in response to the original question:
Wicca is a very specific religion with very specific beliefs and practices. It was the result of the work of Gerald Gardner in the 1940's and 1950's and now has followers all over the world.
Pagan is an umbrella term used to describe many different religions such as Asatru, Druidry, Heathenism, Hellenism, Kemeticism, Celtic Reconstructionism, some forms of Witchcraft, and of course Wicca.