According to Denise of Go Planet Earth, a dye is soluble (dissolves) in water, oils, alcohol, or glycerin. The color of dyes can change when put in a high pH environment such as cold process soaps. For example, many blues will turn pink in cold process soap. Our dyes are all "coal tar" dyes, which means that they are chemically manufactured. They are also all approved for use in cosmetics. In general, dyes are brighter in color, and color "bleeding" can be a problem. Dyes work exceptionally well in single color pours. Single color pours means you are only using one color when pouring soap base into a mold. Color bleeding is only an issue with dual color soap pours in the same mold OR when embedding soap shapes."
"A pigment does not dissolve in water or oil. This means that your transparent applications (melt and pour soap, bubble bath, shower gel) are a less transparent (less see-through). Sometimes a color can be a "dye" when it is in water (it dissolves in water) but a "pigment" when it is in oil (it does not dissolve in oil). The positive side to pigments are that they are "non-bleeding". In other words, they won't stain or bleed into surrounding areas of your soap project. Since pigments are heavy and don't dissolve, they will fall to the bottom of the bottle if you mix them with liquid applications such as liquid soap. Liquid products that are heavy or thick enough (a heavy lotion or cream) will stay suspended with no problem. Many pigments are approved for use in cosmetics and a good number are made from earth minerals and termed as "inorganic" colors. There are a number of inorganic color additives used in soap and cosmetics: iron oxides (browns, blacks, reds, etc.), ultramarines, chromium oxide green, and a variety of whites such as titanium dioxide."
If you are interested in purchasing pigments or dyes, you can visit Go Planet Earth's website to purchase colorants for your melt and pour soaps.