Magic in 5e D&D is divided into arcane and divine, with psionic being the figurative cousin twice-removed. I discussed this with two of my friends on the Discord of Many Things – ImFromNASA and
tiredmoieties – and this is a rough take on the ideas we came up with for how scholars within a D&D world may interpret these three studies.
Magic is, at its most fundamental level, is the distortion of the natural state of things - the warping of reality. Traditionally we distinguish mages by where they take magic from: for example, druids take magic from the latent power of the natural world, whilst sorcerers are themselves producers of magical distortion.
The methods by which individuals seek to create distortion can also be categorised. These refer not to schools of magic, but instead schools of philosophy and ideology: states of viewing the world through which magic is magnified. The effect is similar to that of light refracted by different shaped lenses; the light – magic – is the same force, but the lens – an individual's philosophy – shapes how the magic emerges on the other side.
The most common of these mental states is that of Arcane magic. Arcanists view magic through the lens of trying to understand magic itself: breaking down the world into its fundamental components and learning how to reorder and reshape them. Spells, rituals, and incantations are all attempts at recalling the equations of creation. It is a form of magic that requires intense research and understanding of multiple fields of knowledge (unless of course you're a sorcerer who simply has an innate understanding of the way they may interact with the world, or a warlock who has such knowledge directly implanted into their minds).
Divine magic views magic through the lens of belief and faith. The individual views the world through a set of ideals and values, as well as through the pre-conceived notions of what their focus of faith (be it god, patron, ideal, or idol) is capable of. The individual then evokes this power, using their belief as the focus of magic. It is due to the nature of belief that clerics and the like can dip in and out of arcane power; as their faith wavers or is tempted, so too does their power. This also goes on to explain why different deity worship evokes different powers: the idea of what magic
should do within a cleric's faith is just as influential as what magic theoretically
can do.
Finally, there is the most elusive of magics: psionics. For many it is not considered true magic, due to the lack of material components or rituals. However, this is not due to the absence of magic, but instead due to how psionics is channeled. The Invisible Art is the inverse of Arcane magic: instead of focusing on known truths about the world, psionics focuses on the known truths of the self. It delves into one's own mind and notions of the world, using magic to then shape reality to fill in the gaps where reality doesn't quite match up. A psion's power is drawn from the understanding of the self and the self of others, allowing them to connect to the minds of others and free themselves from illusions designed to cloud the truths of their own senses from them.