Sheet metal screws have sharp threads that cut into materials such as: Plastic, Plexi Glass, Wood, and sheet metal. Sheet metal screws are also the go to fasteners for use with plastic wall anchors in drywall.
Tapping screws are considered externally threaded fasteners that "tap" their own mating threads in metallic and non-metallic (such as plastic) materials.
Tapping screws, especially Type A, are referred to as "sheet metal screws" because one of their first applications was in ventilation ducts made of sheet metal.
They also make excellent fasteners for attaching metal hardware to wood because the fully threaded shank provides good retention in wood.