Well said, Robert Ramsay. Mysticism is not magic, per se, at least not historically, but can be seen as preparation for magic - though even these distinctions are also not absolute. Systems like New Thought, Chaos Magic, and other more transcendental approaches work effectively without all the clutter and bric-a-brac of traditional sorcery or goetia. These practices focus on pure manifestation. Great stuff!
But how we discuss these concepts depends greatly on where we enter the conversation and when our individual understanding of "magic" was formed or informed.
Classically speaking, there is a cosmological division: the realm "Above", the Supralunar world, where there are no gods, no spirits, no demons—just "God," or in a Buddhist or Chaos Magic sense, pure consciousness and awareness, including what we might call the "subconscious."
Mysticism, then, is about enhancing and refining one's relationship to the Mystery - in Catholic mysticism this is called "theosis. " But no need to take those myths literally, but I recommend the belief SOMETHING real is going on behind it all - whether you conceive of that as the Divine, God, the gods, or your own subconscious, however you choose to define your cosmo-conception,. This is where it's centered on connections, totality, communion, and direct experience of the transcendent, or minimally more than just your everyday boring personality.
In contrast, the classical cosmological conception distinguishes what they called "magic" - by which they meant practices like sorcery, witchcraft, and necromancy, NOT mysticism, prayer, or connection with the Divine. This classic understanding "practical necromancy" works with sublunar elements, forces,
magia materia and spirits. It doesn't have to be about Oneness or unity at all, and can be employed for various purposes, say, to heal or to harm, to protect or to curse - and as being fundamentally about getting things done in the material world, rather than seeking connection,. . You can be as nasty as you want here. This is an externalized practice in the world of STUFF beneath the moon
Modern "witchcraft" systems like Wicca - which owe a huge debt to New Thought -and is basically "wishcraft" with candles - have confused these two domains together, to the detriment of both, in my view. By blending mystical practices (which are about connection with the "Divine" or "transcendent consciousness" ) with practical magic (which is about working with sublunar forces to achieve tangible results), have muddied the waters and lead to idiotic, and nasty pseduo-religions like BALG dark fluff.
For a useful historical understanding of the supralunar and sublunar realms - "The Above" and "The Below" - and how these cosmological divisions shaped classical approaches to mysticism and magic, I highly recommend Skinner's book:
Michael Psellus on the Operation of Daemons: De Operatione Daemonum