Psionic and primal, and arcane and divine, are power "sources".
These sources are tags. They have no rules in themselves but other rules might refer them.
It occurs to me, a SETTING can create a rule for a source. That source rule is true for that setting, but is untrue for other settings.
Examples of setting source rules.
Psionic versus arcane. In the Dark Sun setting, psionic is safe magic while arcane is dangerous magic. Arcane mages divide between self-suppressing minimizing risk, versus wreckless destroying the planet.
Primal versus divine. In the (3e) Forgotten Realms setting, gods control divine magic and at their discression, their "portfolio" can turn the divine magic on or off. Moreover a god depends on its worshipers and loses power if the number of worshipers decline, and can have their portfolios stolen by someone else. By contrast, primal magic derives from nature collectively.
Arcane. I might have for my setting, only the arcane power source uses material components, and must do so. The flavor is Greek (Hellenistic) protoscience, where its "magos" studies how to exploit the different properties that are inherent in different objects. For example, according to ancient scholars, the agate stone is known to prevent the spread of poison. Alchemy, potions, and "magical ingredients" are an important part of the arcane protoscience.
A SETTING can say there is no is no transparency between psionic-and-primal versus arcane-and-divine. So, primal can dispel primal or psionic effects, but cannot dispel arcane or divine effects. And so on. The setting can make this rule, but the core rules cannot. The core rule default is all of these magical sources interact with each other normally. But in the core rule, each source is a tag, and a specific setting can make up special rules for that tag.