A self-tapping screw can accurately be described simply a tapping screw, but is also regularly referred to as a sheet metal screw, since they are used so heavily in the sheet metal trade.
Whichever name is used, a self-tapping screw (or sheet metal screw), is designated as such because it contains form mating threads (thereby “tapping” the threads) in a pre-drilled hole into which they are driven.
A self-drilling screw is a type of self-tapping screw that also features a drill point. The sharp drill point will both drill a hole and form the mating threads in a single operation.
So where does the confusion between terms come in? In many cases, the person specifying a this type of screw will interchange the terms self-tapping screw (or “Self-Tapper”) with self-drilling screw, but a screw is only a self-drilling screw when it will drill its own hole.