Anywho, I think while psionics could be called a kind of magic, it's almost always presented in a particular way: psychic powers have scientific or psuedo-scientific (or at least comic-book science-y) explanations. They do not have religious (in the Western sense) explanations: the gods are not involved.
Beyond that, there's some tendencies associated with psychic powers in popular media. Some abilities are common (telekinesis, telepathy, pyrokinesis), some are almost never seen (summoning demons, raising the dead). Some trappings are common (crystals, mental effort) some are almost never seen (arcane texts, magic wands). But there's a pretty big middle ground of "general magic stuff" that also applies to psychic powers.
If we want to tap into the history of psionic powers in Dungeons and Dragons (tm), there's a lot of stuff to call on, some of which is crunch (power points, psionic attack modes, psychic disciplines) and a lot fluff (how these things are named in contrast to how other magic stuff is named). Plus an array of specific psionic stuff to mine like powers and magic items.
None of these lines are hard barriers that must not be crossed. On the other hand, ignore these tropes too much and you won't have something that people will think of as a psion, which would result in a rather disappointing take on the idea.
For my money, psionic powers are a different enough kind of magic to warrant and require a new class. I'm not in favor of treating psionic powers as "not magical" in rules terms, because that creates a bunch of loopholes that tends to wreck game balance - it's really hard to tell an engaging story about a character who's attacks cannot be defended against by most of their opponents.
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