The difference between Magic user and Witch

Magic user as a noun (fantasy):

One who uses (or has skill with) magic.

Witch as a noun (archaic, _, outside dialects, and, Wicca):

A person who practices witchcraft; a woman or man who practices witchcraft. A woman who is learned in and actively practices witchcraft.

Witch as a noun (derogatory):

An ugly or unpleasant woman.

Witch as a noun:

One who exercises more-than-common power of attraction; a charming or bewitching person.

Witch as a noun:

One given to mischief, especially a woman or child.

Witch as a noun (geometry):

A certain curve of the third order, described by Maria Agnesi under the name versiera.

Witch as a noun:

The stormy petrel.

Witch as a noun:

Any of a number of flatfish: (Torbay sole), found in the North Atlantic. (megrim), found in the North Atlantic. , found near New Zealand.

Witch as a verb (obsolete, intransitive):

To practise witchcraft.

Witch as a verb (obsolete, transitive):

To bewitch.

Witch as a verb (transitive):

To dowse for water.

Witch as a noun:

A cone of paper which is placed in a vessel of lard or other fat and used as a taper.