Stampin' Up! has both Jet Black StāzOn Ink Pads and Tuxedo Black Memento Ink Pads in their Annual Catalogue. Put simply, the biggest difference between these two black inks is that StāzOn is a solvent-based ink and Memento is a water-based ink.
In the world of ink, the term solvent is used to mean any ink that is not made with a water base. Because StāzOn is a solvent-based ink, it is permanent and can be used on paper as well as any non-porous surface, like metal, plastic, transparencies (Window Sheets), glass, and ceramic. Also, stamp with StāzOn if you want to watercolour as this fast-drying, solvent ink will not bleed.
A water-based ink is any ink which uses water as the base to carry the pigment (colour). Memento is a good all-purpose water-based ink for stamping on most paper. Also, stamp with Memento if you want to colour with Stampin' Blends as this water-based ink will not interact or bleed into these alcohol-based markers.
Here's a quick tip, when using these two black inks, think of StāzOn as similar to a Sharpie permanent marker, and Memento as similar to Felt Tip colouring pens.