I wouldn't say they taste the same - there's an overlap area with some where there would be confusion. But there will be whites that are simply not likely to be confused with reds, and vice versa.

Though if you handed a white wine from that overlap area and colored it to look like a red. I'm pretty sure all but the experienced blind tasters would just accept it as being a light red.

I am studying Enology at the moment, and have no doubt that I could be confused with the right wine. My pallet just isn't good enough. But having done enough bind tastings in the past I really feel like some wine types really do stand out enough to be recognized.