Many people add a "k" to magic to distinguish true magick from slight-of-hand and stage tricks.
Magick is a broad term given to the ability to make events occur in accordance with one’s true Will by the application of sufficient energy.

In other words, magick is the direction of energy to a desired goal or purpose. It is a manipulation of the more subtle forms of energy which science is just beginning to understand.

Magic is a very general term which describes many branches or areas within it's self.  For example, one could compare the broad term of magic to the broad term of medicine.  In the medical field, there are various things someone can specialize in.  Whether it be Cardiology, Pediatrics, or Surgeon just to name a few.  Accordingly,  there are many very different and specialized areas within magic, some include Elemental Magic, Sympathetic Magic, Herbalism, Aromatherapy, Healing, Shamanism and many others.  One of these areas which is generally thought of as the spell casting area of magic is Witchcraft.

Witchcraft
 

Witchcraft is a branch of magic that also deals with healing, protection, fertility, curses, hexes and the likes.  It is a branch of magic that is centered on techniques to improve the life of the practitioner and those around them.  Those who practice Witchcraft or Wicca also tend to be of the Pagan religion, but this is not a requirement perse'.