Both colors are considered "whites" for purposes of showing chinchillas.
A mosaic is a chinchilla with a white gene. The base color of this chinchilla is white, and they can have grey / silvery markings over their body. Mosaics have dark ears. The chinchillas pictured below are all mosaics.
A pink white is a mosaic with a white gene and a beige gene. They also have a white base, and the have beige markings over their body. Pink whites have light ears, which tend to look pink, hence "pink white." The chinchilla pictured below is a pink white.
That pink white (above) has very little beige markings. However, just like the mosaics, pink whites come in all sorts of markings, from almost all white, to dark beige markings. For example, this picture (from chinchillas.com) is also a pink white.