Witchcraft is one of many names used for a magical practice. Magic, as part of the occult, is a general term that encompasses all aspects of practice and could mean socerery, witchcraft, or other mystical beliefs that include spells and castings to spirits, nature deitys and demons.
Magic, is a series of techniques to control or manipulate the spirit world with your will and intent to obtain an outcome that you desire. Witchcraft is simply just another name for magic.
The terms magic and occult are often used interchangeably by contemporary practitioners of magical practices or religions. Magic has traditionally been seen as distinct from the occult, which literally means “hidden knowledge.” The occult is the study of various magical practices. The occult defines a series of beliefs and practices that are outside standard scientific reasoning. The purpose of occult practices, like magic, is to influence the normal course of events through nonordinary means.
Many countries and cultures have their own branding or various names for witchcraft all employing magic as a technique to manipulate the spirit world.
Magic and religion have traditionally been as two separate entities. Religion is viewed as more complex than magic, involving the worship of and prayer to the divine or unholy deitys who can choose either to answer or deny those prayers.