Their etymology is different.

Word stupid comes from Latin stupere - “be amazed or stunned, be astounded”.

Word idiot comes from Greek idios - “own, private, layman, ignorant person”.

So, stupid person is a person, who’s though flow is blocked by some internal or external event, for example by “wow effect”. This state is usually recoverable.

On the other hand, idiot is somebody who’s though flow is blocked by his Ego/Superiority, flow is not only blocked, but could not change. Due to his behavior he is ignored by other people, he could not change himself due to ignorance. It is very difficult to recover from this state for given individual. That’s what Dunning–Kruger effect - Wikipedia describes.