Shamanism is the parent who was captured and released by OG Neighbours. They came back very...strange. They perform magical services for their communities, often at the cost of "favors". Sometimes those "favors" look like mystical training, and sometimes they look like magic.
IMO, "sorcerers" are also intentional creations of the Neighbours; Pratt would disagree.

Mysticism is the child whose fey kidnapping was prevented by "friendly" aliens. Much of what they do looks like things shamans do, but in a different context. They tend to be more lucid, and can often teach useful skills to other people. Pure mystics generally don't do performative magic, but magic often happens around them, and is usually seen as benevolent.