Olgar Shiverstone
Legend
Why does this distinction really matter, given it all looks like magic? Why is telekenisis with "mind powers" meaningfully non-magical in a world where a wizard also moves objects about without touching them? Isn't this all "Unexplained mysterious physics-breaking stuff that a few can do"?
In "in world" or "in character" terms, I don't think the distinction matters at all.
In game terms -- from a rules perspective, that is -- a decision on one course or the other is necessary. My objections to psionics are all based on game rules and structure issues. If a player in game told me "I want to recolor my wizard as a mind-mage" and didn't touch the mechanics, I'd shrug and say "have at it."
I'll also admit to a deeply-ingrained, 1E-based prejudice against psionics. An appendix of the PHB touched me in an unnatural manner ...