Nikon does not appear to make an HB-45 II lens hood. If you look at the images, it appears that they are attempting to sell a third party product under the guise of being an upgraded official product. If you look at Nikon's product page, the HB-45 from Nikon is the officially supported lens hood that is designed to be used with your lens.

As szabolcs pointed out in the comments, the lens petal hood won't even work properly since the front of the lens itself rotates which would move it out of position and would result in inconsistent results that would cause a deterioration in image quality. Personally, I'd rather trust the style that the manufacturer (who knows the optics) built to work properly with it. The third party one may or may not be particularly effective or well built. I'd be particularly concerned by the fact they were trying to make people think their product was a newer Nikon product. If they are dishonest there, where else might they be dishonest?