Mystical, mystic, anagogic, cabalistic are comparable when they denote having a meaning or character hidden from all except those who enjoy profound spiritual insight or are spiritually initiated.
Mystical and mystic, though often interchangeable, can be distinguished in use. In general, mystical suggests comprehension of something beyond the range of the perceptive or ratiocinative powers; its use therefore often implies belief in the possibility of such comprehension and the word variously connotes penetration into sacred mysteries, holiness of life, idealism, detachment from material concerns, ecstatic contemplation, or spiritual rapture.
Mystic is appropriately used when one wishes to avoid these special implications of mystical or to suggest others more in keeping with a rationalistic or skeptical point of view. Therefore mystic often imputes to the thing it describes:
(1) an occult, esoteric, or visionary character.
(2) a mysterious, enigmatic, or sometimes nebulous quality.
(3) a connection with magic or the arts of magic.
Often its basic denotation is completely obscured and it means merely unintelligible, unfathomable, or incomprehensible.
Anagogic refers basically to an ultimate underlying meaning, especially in the Bible, perceptible only to those of profound spiritual insight.
Cabalistic in its primary meaning applies to a secret interpretation of Scriptures (Cabala ) held to have been revealed to Moses and handed down orally through a line of chosen Jewish rabbis. The system came to be used by medieval magicians and sorcerers. Both aspects color the extended use of cabalistic so that it sometimes comes close to mystic in its connotations, but commonly it is closer to occult or magic.