A philosopher is technically a lover of wisdom, someone who seeks understanding and a greater comprehension of reality. They revel in shining a light into dark places, and are characterized by curiosity, profundity, and an eager desire to improve their character.
A mystic is someone who lives their life according to a greater Reality than can be immediately or physically perceived; but they do so in the sense of a drop moving along with the Ocean. Through love and intimate communion they wish to perceive Reality directly, not only through the lens of the mind or perception. They seek dissolution and combustion in the flame of love – moth-like – rather than the sober gaze of the philosopher.