Pigment resists fading. Dye fades quickly in sunlight, including sunlight coming through a window. So when staining any object that will receive direct sunlight, always use stain containing only pigment.
Because pigment settles and dye doesn’t, you can easily test for pigment or dye by dipping a light colored stirring stick to the bottom of a can of stain after you have given all the pigment enough time to settle (usually a week or longer).
If the upper part of the stick is colored, the stain contains dye. If you can lift solid material off the bottom of the can, the stain contains pigment. If both, the stain contains both pigment and dye.