Worldbuilding

Psionics are fast, magic is slow. Have magic require rituals and concentration to enact whereas psionics are instant actions.

You could make magic defy the laws of physics, whereas psionics cannot, e.g. magic can create something from nothing, stop time, etc

If your setting supports it you could make magic bound to supernatural entities, where all users make bargains with demons or whatever else to do magic. These bargains could be 1 time (i.e. you make a 1 time bargain to cast 1 spell) or could be long term/permanent contracts.

The D&D model splits traditional magic into Vancian Magic (memorizing your spells daily) and Power Points (cast anything you know with your energy reserve). There's also a more cosmetic differentiation, with traditional magic being a combination of words, gestures, and material components while psionics require a certain emotional state (joy, anger, sadness) and produce some sensory output (bizarre lights, sounds, or smells). This is a very mechanical approach, but I think it lays out a good broad guideline for drawing distinctions between systems.

To go further, I do think its a good idea to root each system in a fundamental theory of origin.

In the games Rifts and Shadowrun, the emergence of Arcane Magic stems from the appearance of Leylines - large rivers of magical power that crisscross the planet and converge to form nexuses of intense power. Magic is strongest in proximity to these energy flows and weak outside of it. Wizards and Technomanciers congeal around these rivers and nodes of power, fighting over them to harness their workings. Mage: The Awakening has a similar mechanic (Nodes) from which a practioner harvests the Quintessence/Mana that makes performing magic easier. Dark Sun (a 2e D&D setting) suggests that Arcane users pull the lifeforce out of living things to perform their workings, blighting much of the planet through excessive misuse and scorched earth conflicts.

Psychics could be distinct from Magicians in that they have their own internal reserves of power. While they may initially harness their powers from Leyline / Quintessence exposure or emerge as a bloodline of otherworldly creatures native to leylines and nodes, they would become fonts of internal energy as they mature. Monks channeling their inner Chi, Lycanthropes that convert solar/lunar energy into forms of supernatural transformation, and guys with really big heads who can lift things based on their whims all pull from a limited but portable internal engine of power (or harvest it from people in their immediate vicinity).

Magicians become a kind of Arcane Technician, building giant magical water wheels or penumbra-piercing radio towers that can harness the ebbs and flows of ambient ether. They do incredibly workings confined to particular locusts of power. But the farther they get from these power centers, the more impotent they become. Veterans rival one another for valuable turf, while amateurs forage in the wild for untapped veins of power to call their own. Magical power tends to be elemental, lending itself to industrial applications with enormous surplus yields in the hands of singularly gifted individuals - reshaping large bodies of earth or air or water, powering industrial engines for manufacturing, defying gravity, providing heat or refrigeration/illumination/electrification to large areas. This can transform their territories into pocket utopias, but also lend themselves to expansive military conflicts. Magi enjoy a kind-of Sith Master/Apprentice relationship, with an undercurrent of paranoid distrust running between the two (the Master fearing usurpation by an overly talented Apprentice, the Apprentice fearing they are a disposable cog in the Master's grand design). And as a kind of scientific study, its a power anyone can potentially wield, leaving ample opportunity for closet dabblers and minor practitioners to exist in the shadows of Wizard Lords.

Psychics can perform minor workings individually by harassing their limited inner energy reserve. This makes them valuable freelancers, particularly in areas without leylines. Groups of psychics can pool their power through psychic tools or psychic collectives managed by psychic masters, allowing teams or large communities to function at scale comparable to individual magicians with access to leyline energy. Low level psychic powers tend to be tools of communication and cooperation - telepathy, psychic memorization/recall, therapy/pain relief, psychic healing, minor physiological enhancement. Larger workings involve coalitions of psychic professionals, cults of like-minded devotees, or pools of willing sacrifices to a higher cause, but mostly extend the basic abilities (broadcasting mental signals internationally, divining the past/future through psychohistory, exerting mental influence at a community level, channeling the strength/intelligence of a community into a single individual). This means a hogpog of close knit interdependent communities, secret societies, and informal guilds or conglomerates of enhanced individuals. A swirling morass of confederacies and coalitions, where the politics of the moment revolves around building the largest and most sustainable collectives.

One more wrinkle might be that Magicians - recognizing Psychics as portable power sources - may partner or exploit this ability to get around their own limitations. This creates some symbiosis between the two, with psychics potentially parlaying their ability to generate magical power internally to politic with magicians, more unscrupulous magicians finding ways to parasite off populations of the psychically awakened, and the accumulated history creating a virtuous/villainous feedback loop of cooperation/persecution.

As point of comparison, in the Weis & Hickmen book "Darksword Trilogy", a particular variant of magic user exists entirely as a vessel for magical energy but lacks the ability to perform magic themselves. They become a kind of priesthood instrumental in the more overt magic users' capacity to rule. On the flip side, Psychic Vampires in Rifts regularly sniff out active psychics as their preferred prey. They are so indispensable in this task that they form the backbone of certain fascist governments' anti-psychic police forces.

The internal/external oriented powers inform the propensity of larger community of power-users, the conflicts/compromises made between sects, and the general public attitude towards practitioners.

I think forms of specifically elemental manipulation/alchemy are good examples. Could psionics also move/manipulate elements? Perhaps, but not at the scale/intensity of someone harnessing that power vs moving it with brute psionic force. Additionally, things like astral realms could be locked behind magic as being sources of power that psionics cannot access since their power is primarily mental.

Maybe magic needs some key component that is quite obvious like the caster having to draw runes to cast magic, or perform elaborate hand movements, or having to somehow "calculate" e.g. how to move magic waves.

Meanwhile the maximum you would see from a psionics user would be a concentrated face.