If you ever have the chance, try some raw sugars from places like Mauritius. There are many kinds, but they all come from sugar cane and their taste profile is wildly different. The "kind" of sugar depends on what stage of process it was taken. My personal favourite is molasses sugar [1].
I am not sure if they change the recipe apart from the sugar but it is noticeable.
Some people can taste the difference (double blind and everything - I'm not sure if anyone has done the tests). I would think the water used would also make a difference.
It's about as subtle as the difference between velvet and silk to your finger -- I can see how you'd confuse them if you weren't thinking about it, but there's no way you'd stay confused if you paid attention and practiced.
Surely someone does it right, somewhere.