Magic Feather vs. Placebo Effect

"Supertrope to Placebotinum Effect, and of course this is the Placebo Effect."

This phrase is from the description for Magic Feather. If this isn't a distinct concept, why is it a distinct article?

It seems like a magic-specific variant, like a subtrope; it's just worded really poorly. But the Placebo Effect is supposed to be for medicine specifically, right?

Placebo Effect is where the character believes the feather to be effective, regardless of actual effect.

Magic Feather is where there's an actual effect, despite the feather not doing anything.

If anything, Placebo Effect seems to be the supertrope, since Magic Feather seems to always include the belief. Which, to be fair, is understandable, because it's easy to believe an effect that actually happens. It's just misunderstanding the source.

I have more trouble placing Placebotinum Effect, though. I don't see why it's a subtrope of Magic Feather, rather than just another name for it.

Placebo Effect is a real world term, utilized particularly in medicine. Magic Feather is specifically when a character is granted abilities with an item but only via the Placebo Effect, and they have to undergo a Test Of Character to see if they can manage without it.

Placebotinum Effect appears to be more closely related to Clap Your Hands If You Believe, where it's literally the power of belief that allows something to work.