"Magical" vs. "mystical" and "mystic" vs. "mystery"
Magic refers to the use of various techniques to control nature. Magic may invoke the supernatural-that's probably why confused with mysticism. But magic is practical-not concerned with knowledge of or union with a higher sphere.
A mystery is something that you don't understand. In the plural, mysteries refers to "the skills, lore, or practices that are peculiar to a particular activity or group and are regarded as the special province of initiates" (AHD 4). Thus one speaks of the "Eleusinian Mysteries."
Mystic and mystical are adjectives
both of which may refer to mysteries in the religious sense. Both
may also refer to mysticism, which has to do with spiritual union with
a transcendent supersensory being or sphere. It is not clear that
the Eleusinian Mysteries in ancient Greece were a form of mysticism.
muein "to close the eyes"
mustês "initiate," someone who has closed his/her eyes