Very nice. Well done.
They're technically the same character. Her appearance was retconned at some point. I do like the idea of an alternate universe version of a character tickling another variant of herself, though. It's a cute concept.
And no, Daisy is an entirely different character. Daisy's origins are murky, but she was the damsel in a different line of games that also starred Mario, and has since been clarified as a unique character. The confusion stems from Toadstool's retcon name to peach in the west, and also the change from her original design.
But hey, that's what multiverse theory is for.