Dye Inks are fast drying, so won’t smear or smudge your project, but dry too fast to use for embossing. Unless you are using waterproof dye inks, it will run if used with wet coloring techniques, like markers, watercolor paints and pencils, etc.
Pigment Inks take a while to dry so will smear or smudge if you aren’t careful, but are good to use as a base for heat embossing. This type of ink is popular for scrapbooking and other projects that will be kept for a long time because it is fade resistant.
Solvent Inks are permanent inks that can be used on almost any surface, including paper, of course, as well as plastic, glass, metal, transparencies, and more. It will not bleed so can be used with wet coloring techniques, like markers, watercolor paints and pencils, etc.
Chalk Inks produce a softer look than other inks. They are available in both dye and pigment inks. (ColorBox and Stampa Rosa's Fresco are dye inks, Ranger Antiquities are pigment) Usually small sized stamp pads, they are easy to use for inking any size stamp, as well as for inking edges of paper.
Versa Mark is not really an ink, but a watermark, or resist ink. A few of the techniques to use it for are:
Stamp on colored cardstock, creating an image in a slightly darker tone than the paper color for an interesting look, color a stamped image with chalks, or use as a base for heat embossing.
Like I said, this is just a brief summary of what I have found. I think it is pretty helpful information. I hope someone else gets something out of it too.