I found this on www.stampendous.com and thought it would be a handy reference.
Dye inks are water based, non-toxic, washable, and many are child safe. Dye inks are trans- parent and will blend easily and dry quickly on most matte and glossy papers, but will run if wet again. Dye inks do fade. Dye inks do not work well on clear stamps.
Pigment inks are water/glycerin-based, acid free, non-toxic, fade resistant and more opaque than dye inks. Pigments are not easily washed out of clothing. Pigments will not dry on glossy or non-porous papers without embossing. Once embossed they are permanent and can be safely watercolored. Their slow drying property makes pigments ideal for heat embossing. Pigment ink is available in pads and markers.
Craft inks are acrylic based ink, acid free, non-solvent based, non-toxic and water soluble until completely dry or heat set. Once dry you can safely watercolor over them. You can use them on fabric, wood, paper mache, foam, leather and a variety of other surfaces.
Permanent inks are solvent-based and require special cleaners to remove from the rubber. They will be permanent and water-resistant on most non-porous surfaces. They are quick drying and are ideal for stamping on glass, plastic, metal and fired ceramic pieces.