What is the differences here: “substance dualism, the version associated with Plato and Descartes; property dualism, associated with the likes of John Locke, David Chalmers, and (the early) Frank Jackson; and the hylemorphic dualism”?
The links Peter Plato has given are good.
In brief:
In substance dualism, the body and the mind (or soul) are two distinct substances (basically independent entities, though what a substance is will depend on whose theory you are talking about), the mind being immaterial.
In property dualism, there is just one sort of thing: matter construed physically. But matter can have two sorts of properties: straightforward physical ones as well as mental.
In hylomorphic dualism, the soul is the substantial form of the body in the sense that substantial forms are understood in Aristotelianism/Thomism. For that reason, it’s a bit improper to talk about the “body” as though it is distinguishable from the soul. All substances (even nonliving ones) are hylomorphic (matter-form) compounds; the human substance is just a specific case. A form specifies not just things like shape but the characteristic activities of the substance. So the human soul accounts for the intellective activities as well as the basic material activities of humans (ie. digestion or even nonliving dispositions associated with being material, like mass); there is no presumption that a form is anything special. But, it is claimed, the intellective activities of the soul do not require matter, so the human soul subsists unlike other forms and souls. (Whether this last move has been sufficiently argued for is actually pretty widely disputed in the literature.) (Another benefit of hylomorphism that is tough to articulate in a short space is its causal pluralism; hylomorphists employ formal, efficient, final, and material causes, all of which play into philosophy of mind, whereas most contemporary theories just admit something resembling efficient causality. This allows hylomorphic dualism to address a number of problems; it does not face an interaction problem, as does substance dualism, and it does not relegate the mental to the epiphenomenal, as arguably even most materialisms do. I’d argue that they also are what make possible an explanation of libertarian free will, though that is a very complex issue.)
Substance and property dualism (as a general rule of thumb) take “qualia” and consciousness (and maybe intentionality) as the characteristic marks of the mental, whereas hylomorphism takes intellection and abstract, general thought as what is distinctively human and resistant to material explanation. (However, hylomorphists are more likely to allow finality, which resembles intentionality, in their general metaphysics, so they would likely admit a difficulty for materialism there.)
Aquinas’s philosophy of mind has been interpreted in a few different ways. Feser and Oderberg have spearheaded hylomorphic dualism in the last decade, and I think it’s the most plausible reading. A related subject of dispute is whether Aquinas’s philosophy of mind should be construed as a dualism (Jim Madden, for example, just calls it hylomorphism, but his theory is pretty close to Feser and Oderberg’s). Some others have considered it to be a non-Cartesian substance dualism, construing the form as a sort of substance. (One can work such a theory out so that it is basically equivalent to hylomorphic dualism, or it could be somewhat different. However I think that categorization has more to do with philosophers simply not deciding to create a separate designation.)
William Jaworski has also defended something called “hylomorphism.” He is a Catholic philosopher, I believe, but he mostly defends it as a stronger form of emergentism with the benefits of causal pluralism; he tends not to defend the more historically characteristic features of the theory, like the immateriality of the intellect. This may simply be the context of his defense, though.