Summoned, I appear!
Ok, in terms of in setting, the principal distinction is that psionic powers are socially accepted. Psionic academies exist in every city-state. Many people (though not all!) have wild talents, making psionic abilities a commonplace part of everyday life.
Arcane magic, on the other hand, is widely believed—correctly—to be a contributor to the devastation of the world. Sorcerer-monarchs practice it, and everyone knows that they are bad news. They also have defilers who do their dirty work, and those are bad people, too. When someone reveals that they practice arcane magic, for the typical Athasian this is akin to admitting that you’re a terrorist. You wield a kind of power that is used by the dictators of the world, and which was used recklessly in a way that turned the world into an unforgiving desert.
Psionics are also very covert. You think, you concentrate, you shape your Will with the Way, and you manifest an effect upon the world. If you’re cautious, you can slip into someone’s mind and nobody will ever know. You can fold space to travel long distances, or sense upcoming hazards, or realign your body to heal terrible wounds, all with concentration and meditation. Unless you use a concentration focus (which is purely a personal aesthetic choice for most of the psionicists out there), your abilities have no overt signs of use: You don’t chant words, you don’t wave your hands in weird gestures and sway your body back and forth, you don’t produce and handle odd implements and objects.
Arcane magic is overt, especially if you use the rules from Dragon Kings. Casting a spell frequently involves speaking strange words that are obviously not from a common language. Many spells rely upon making odd gestures and body movements. Quite a few require you to handle curious little objects, which mysteriously vanish or crumble (or, in some cases, you consume them). It’s possible to make your spellcasting secret—you can make your somatic gestures appear to be stumbles, odd twitches, accidental movements, using the Somatic Concealment nonweapon proficiency—but if people are paying attention, they will eventually catch on that you’re doing something strange. And, of course, if you are defiling, that’s almost impossible to hide. (In the Revised 2e edition you can do your defiling as you prepare your spells, but that still leaves a scar where you did your spell preparation; in the original 2e, you always defile where you cast the spell, which makes what you are doing very obvious).
In terms of ludonarrative harmony, psionic powers function through concentration, mental exercise, and internal focus. A psionicist relies on holistic body awareness and deep wellsprings of an opened mind, and these result in abilities that clearly demonstrate mind-to-mind contact, ability to glimpse the future and past, twisting of space and time through higher dimensional cognition, manifestation of forces without physical origins, and total control over the body’s functions. Conversely, psionic powers find it difficult (though not always impossible) to perform functions like reanimating or raising the dead, communicating with plants, binding extradimensional creatures (they can be summoned from other dimensions but there are no “protective circles” or “bindings” other than telepathic domination), conjuring matter (like a wall of stone), or dispelling magic.
Arcane magic, on the flip side, is extremely flexible. It excels at conjuring forces and matter, building magic defenses (whether force-barriers against physical attacks or magical abjuration against spells and extraplanar powers), summoning creatures, making things invisible or intangible, and enhancing or diminishing creatures by giving them unnatural qualities (like haste and slow, or strength, or spider climb). But on Athas, arcane magic comes with a price. In original 2e DS, you were either a preserver or a defiler and those streams didn’t cross (there’s a Sage Advice answer in which it’s mentioned that a preserver cannot “become” a defiler, and vice versa). Later, this was opened up to allow defilers to seek redemption, or to allow preservers to fall to temptation—a dramatically-powerful rules element that supports the notion that every preserver is just one bad day away from becoming another would-be sorcerer-monarch. (This also underscores the social danger: If any preserver is a potential defiler—like Sadira in the novels, or like Oronis, who went from defiling to preserving—then the fear that the general public has for wizards is much more understandable, because even a “good” wizard can break bad.) Arcane magic involves drawing energy from planar interstices by using repeatable phrases and motions, so it is something that people can see and notice, and you risk discovery when you use it. And, of course, defiling is a choice, and one that damages the life energy around you in a very clear and conspicuous way; the rules need to support that when you use arcane magic, there is a chance you’ll be caught, and if you use defiling, it is literally painfully obvious to everyone around you.
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