The difference between Wicca and Witchcraft can be summarized simply: Wicca is a religion whereas Witchcraft is a practise. That begs the questions of what is a religion and what is a practise.
A religion is a spiritual belief system, such as Christianity, Islam, or Wicca. It is a series of beliefs, based around observance to or worship of deities and/or spirits. A practise is something that is done, such as prayer, meditation, or magic. Simply put, magic is a practise and Paganism is a religion. Wicca is a subset of Paganism, and magic/spell casting is the main goal of Witchcraft.
It is, of course, possible to practise magic without being a Witch. There are other forms, such as Ceremonial Magic. And magic can also be part of a religion–some argue that prayer is a version of magic, and that the Wiccan Circle is enacted prayer.
The main difference between Wicca and Witchcraft come with the differences in intent. The purpose of Wicca is to honour the Lord and Lady, observe the turns of the Wheel of the Year, and to pay attention to one’s spirituality. Wicca is intimately tied to one’s relationship with the divine, by whatever faces They choose to show to us. Witchcraft, on the other hand, does not have to involve deities. Instead, it is concerned with the use of spells and herbs to achieve a desired end–healing, love, protection, etc.
Because Witchcraft is a practise and not a religion, it is possible to be a member of just about any religion and also be a Witch. (Of course, different religions have different opinions about the morals of being a Witch, but that is neither here nor there.) The openness of Wiccans and other Pagans toward magic and the unexplained makes it all the more likely that these people will be drawn to Witchcraft. But be aware that not all Wiccans are Witches. Many do not cast spells of any type. Instead, they focus solely on their relationship with the divine and on their quest for spirituality.
There are some Witches who will say that Witchcraft is also their religion. And I am no position to argue with them. But I would like to point out that it is possible to cast a spell without calling upon a deity. (Instead, one focuses the power within themselves or within nature.) There are also Wiccans who claim that all Wiccans are Witches. Here, I am able to argue. I am Wiccan, but I am not a Witch. I do not cast spells, work magic, or work with herbs. My focus is on the divine and my spirituality. Although I will admit to being interested in exploring certain aspects of Witchcraft, and can perhaps see myself heading down that path in the near future. But Witchcraft will only be an adjunct to my fulfilling spiritual path.
It is easy to become confused about the differences between Wicca and Witchcraft. Many books aimed at beginners tend to use the terms Wiccan and Witch interchangeably, and focus just as much on religious holidays (such as Sabbats) as they do on magic and spells. I suspect that this is because many Wiccans eventually find themselves drawn to Witchcraft. Personally, though, I would rather see books for beginners focusing more on the basic of the Wiccan faith, and leaving the exploration of Witchcraft for a later time, if the one decides to peruse that path.
Remember, Wicca is a religion and Witchcraft is a practice. Not all Witches are Wiccan, nor are all Wiccans Witches. The focus of Wicca is on the Lord and Lady, the Wheel of the Year, and one’s spirituality. The focus of Witchcraft is on the casting of spells (magic) and the use of herbs towards a specific end or goal.