Traditional Wicca (ie: Gardnerian, Alexandrian, Central Valley, etc.) is a very specific religion with very specific beliefs and practices. Traditional Wicca requires that one be initiated into a coven. They worship a specific God and Goddess whose names are never revealed to those not properly initiated. Wiccans do see themselves as witches in that they work with magic, but their religion is more important to them than the magical aspects.
Traditional Witchcraft is a form of magical practice that does draw on the forces of Nature. It is not necessarily a religion at all. Some Traditional Witches may be Pagan and may refer to Witchcraft as their religion. How they view the nature of the Divine is entirely up to them. However, many Traditional Witches approach Witchcraft simply as a magical practice and they can be members of any religion or even of no religion at all. I have known Traditional Witches who were Buddhist, Christian, Jewish, Pagan, and even Atheists and Agnostics.
Some forms of Traditional Witchcraft are passed down from parent to child in certain families. But it is possible to learn witchcraft on your own if you are willing to put in the time and effort for the studies.
A good book to start with might be "Witchcraft: Theory and Practice" by Ly de Angeles