There are many overlaps between the two - both employ methods of divination to foretell the future, bot are likely to have an extensive knowledge of herbs and herbal medicine and both believe in the existence of spirits beyond the physical world.
There are however some fundamental differences of belief. A Shaman believes in the spirits of the natural world, they believe rocks, plants and trees all have a spirit in much the same way a Witch would believe a human or an animal to have a spirit. Shamans use their relationship with the spirits of the natural world as a source of advice and wisdom to help them shape their lives.
A Shaman will likely practice the entering into alternate states of consciousness in order to communicate more effectively with the world of these spirits. This can be achieved through meditation, herbal ingestion or music and dance. They may also communicate with the spirit world through their dreams.
I'd say that a Witch works primarily with spirits by calling them into her own environment as opposed to travelling into theirs. This is a fairly broad generalisation as some Witches do "cross the hedge" and in doing so transcend into a world similar to the Shaman. But generally a witch will call upon/conjure/summon/speak with a spirit without altering her own state of consciousness to do so. She will interact with spirits in her world, not theirs.
A Shaman's primary role is one of healing and bringing balance and health to his community. Not so with the Witch. There are Witches who are called to healing but altruism is not a core part of what it is to be a Witch. If you talk to Traditional Witches you will find a clear focus on self interest. The methods of healing also differ. A Shaman believes the source of illness is derived from evil spirits and will focus their healing toward the spirit. A witch is more likely to employ folk knowledge and herbal remedies to tackle the physical cause of the illness and its symptoms. A Shaman may enter the body of the ill to cast out an evil spirit - such a procedure would not be undertaken by the Witch.
Witches in the Wiccan tradition honour a God and Goddess. Again this differs from the Shaman who holds no fixed idea of a governing deity but believes rather that all the spirits within the world have messages and advice to offer. The Shaman looks to nature for learning, a Wiccan will look to her Gods.
A Witch looks to work magic by manipulating the energies of the world around her. The power comes from the intent of the witch. The power of the Shaman comes from the knowledge they gain from the spirits they visit in a trance state. A Witch can choose to work entirely independently of spirit but the spirit world is a much more intrinsic part of Shamanic belief and practice.
This is just a quick overview and I'm no expert on Shamanism which differs greatly from my own personal path. If you are interested I can recommend a couple of books on the subject. Try Plant Spirit Shamanism by Ross Heaven or Shamanic Journeying - a beginner guide by Sandra Ingerman to get you started with reading around the subject.
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