The protagonist, Count Otto Vogelstein, is reading an American book when he notices Pandora for the 1st time.
"It was the oddest coincidence in the world; the story Vogelstein had taken up treated of a flighty forward little American girl who plants herself in front of a young man in the garden of a hotel."Eh... hold on.
"The girl in the book had a mother, it appeared, and so had this young lady; the former had also a brother, and he now remembered that he had noticed a young man on the wharf- a young man in a high hat and a white overcoat- who seemed united to Miss Day by this natural tie."The narrator later mentions the candy-loving bit about the brother of the girl in the tale. It is obvious enough- the fun is spoilt a bit when the narrator tells us plainly that it's "Daisy Miller".
We've got a story within a story.
It can be James's little joke. It can be his warning, or "disclaimer", that the situation may appear to be similar initially, but it isn't- Vogelstein isn't Winterbourne and Pandora Day isn't Daisy Miller. It can be a deliberate contrasting device. Look at the parallels: Winterbourne is an American in Europe, Vogelstein is a European in America; there's a change of space and of environment; there are some prejudiced, insinuating people and Mrs Dangerfield is a kind of Mrs Costello. Then Henry James wants to draw our attention to how different Daisy and Pandora are. Like Daisy, Pandora's a bundle of contradictions, but harder to grasp. Describing her as scheming might be going a bit too far, but Pandora knows exactly what she's doing, and does everything for a reason- she's conscious of all norms and rules, written and not, and does what she has to do to get what she wants, and sees through people (Dangersfield and Vogelstein). In the end, she rises.