Inset sinks sit on top of worktops and Undermount sinks are bonded below the worktop itself.
For a fuller explanation, please see here.
This is the standard type of sink that has existed for many years. The sink is completely self-contained with it’s own drainer board and is fitted above the worktop. The cut out for this type of sink is called an “inset” cut out, and is rough and unpolished, since the edges of the cut-out will never be seen once the sink is dropped in place.
This is a much newer and modern concept of cut out. The stone is cut to the shape and size of the sink (usually cut slightly smaller to allow for an overhang), and the sink is fixed to the underside of the worktop, to give a visually exciting finish. Typically undermount sinks are accompanied with drainer grooves, which are carved into the stone itself.