Magic uses sleight of hand, misdirection, and/or gimmicked objects to create an illusion.
Mental magic is a subcategory of magic. It uses sleight of hand, misdirection, and/or gimmicked physical objects to create the illusion of demonstrating extraordinary mental abilities. (Examples of extraordinary mental abilities include telepathy, influencing thoughts, having a tremendous memory, predicting the future, moving objects with the mind and remote viewing.)
Mentalism uses something other than sleight of hand, misdirection, and/or gimmicked physical objects to portray demonstrations of extraordinary mental abilities. Mentalism may or may not include mental magic as part of the method.
Visual Magic: A magician uses a gimmicked physical object to create the illusion that a physical object disappears.
Mental Magic: A magician uses a gimmicked physical object to secretly discover information about a person, then reveal it.
Mentalism: A mentalist uses a gimmicked physical object to secretly discover information about a person. Then the mentalist uses cold reading to reveal more information that was not obtained by a magic trick. The cold reading is combined with the magic trick to increase the appearance of mind reading.
Side note: If you're looking to hire a magician or mentalist, you should check out the video on the website of Jesse Dameron, Philadelphia Magician & Mentalist.