Grey hair is not actually grey at all; It is hair without any pigmentation, making it appear white. Since grey hair is similar to any other hair hue, a shampoo that is suitable for the hair type, regardless of the color, is sufficient.
The grey appearance of a person's hair comes from their white hairs mixing with their pigmented hairs. That is why people with naturally light locks do not appear to have grey hair as it loses pigmentation. Grey hair is usually associated with older people, but hair can lose its pigmentation at any age because of damage caused to the melanocyte cells, which produce the coloring pigment in hair follicles.