Many people confuse the meanings of Magic and Witchcraft, sometimes using them interchangeably. This is incorrect.
The Twentieth-century occultist Aleister Crowley defined Magic as "the Science and Art of causing change to occur in conformity with Will". That is to say, changing ones conditions or reality as one desires. This is not unlike what people expect to gain from prayer but the approach of magic is the antitheses of prayer. Rather than a request of the divine to bestow some favor upon the petitioner, Magic is the practice of directly participating in the process of change.
Yet there is more to magic than what it can bring. Crowley goes on to explain that "Magick (as he spelled it) is the Science of understanding oneself and one's conditions. It is the Art of applying that understanding in action." In other words, magic is a process of discovering the nature of oneself and ones' true purpose in life.
But this is the definition of Magic, not necessarily Witchcraft.
Historically, the word “Witchcraft” has always been a derogatory term for any practice of magic. It is a slur against those who do not conform to the authority of God and Church. This is because true Witchcraft emerged as a revolutionary response to the cruelty of Christianity and other Abrahamic religions. It seeks to liberate the self from the bonds of cultural and spiritual conformity. It has no higher morality than to do what is right for oneself and holds no concept of good nor evil. Like Buddhism and Taoism, it represents a "middle path" that recognizes that life is never so black and white.
In the twentieth-century, the Neo-pagan movement sought to “reclaim” the term Witch for itself and has made it almost synonymous with “Wicca”, a religion invented in the 1940's by Gerald Gardner. This new definition of "Witchcraft" has blurred the distinctions between magic and prayer in a ways that are confusing and detrimental to both. While Wicca may involve elements of Witchcraft, it is not the definition of Witchcraft. There were no-doubt Witches long before there were Wiccans.
Contrary to the claims of such revivalist traditions, Witchcraft is not “Pagan”. Paganism refers to the systematic worship of ancient gods and goddesses, whereas the underlying beliefs of authentic Witchcraft comprise a world-view known as animism; from Latin anima meaning "soul”, or life". The fundamental ideology of animism is that there is no separation between the spiritual and physical worlds and that souls or spirits exist in all things including animals, plants, rocks, mountains, rivers and all distinguishable aspects of the manifest world. Such reasoning also applies to abstract concepts such as words, true names and metaphors in mythology. The magical concept of archetypes is another example of animistic thought.