What's the difference?
Pigmented stains: These stains color the wood by depositing fine particles of color solids on the wood's surface. The particles, or pigments, aren't absorbed but rather adhere to the wood because the stains include a "binder" – typically a thinned clear wood finish with either an oil or a water base. The pigments accumulate more in irregularities in the wood surface, including pores (and scratches), so these areas will appear darker than the surrounding wood. As a result, pigmented stains enhance contrast in woods that have large pores and pronounced grain, and they'll accentuate any marks or blemishes left after sanding.
Dyes: The particles of color in dyes are much, much smaller than in pigmented stains and are typically dissolved in water or alcohol. Because the color molecules are so small, they are absorbed by the wood and produce a more uniform color, even in tight-grained woods. As a result, they can be used to even out color differences within and between boards. Dyes of different colors can be mixed to achieve the desired tone. Dyes are available in powder form and as a liquid concentrate.
Gel stains: These are pigmented stains formulated to be much thicker. They often are wiped on and off, allowing the user to control the amount of stain left on the wood. Because they sit on top of the wood and the thickness can be controlled, they can be used to blend differences in wood color.
It should be noted that some pigmented stains also contain dyes and that, when using pigmented stains, surface preparation affects how much stain remains on the wood. It’s difficult to get a very smooth, close-grained wood to "take" pigmented stain. For that reason, most experts suggest sanding close-grained wood with no finer than 150-grit sandpaper prior to applying a primarily pigment-based stain.