All-or-nothing is usually used when describing the action potential. It refers to the well-known observation that an action potential always occurs in its full size (i.e., full magnitude of voltage change).
Many physiologists use all-or-nothing and all-or-none interchangeably.
Sub-threshold (or subthreshold) refers to a stimulus that is too small in magnitude to produce an action potential in excitable cells.
In general, a sub-threshold stimulus leads to the depolarization of the membrane, but the magnitude of the depolarization is not large enough to reach the threshold voltage. Therefore, sub-threshold stimuli do not elicit action potentials.
Supra-threshold (or suprathreshold) refers to a stimulus that is large enough in magnitude to produce an action potential in excitable cells.
In general, a supra-threshold stimulus leads to the depolarization of the membrane, and the magnitude of the depolarization is larger than that necessary to simply reach the threshold voltage. Therefore, supra-threshold stimuli elicit action potentials.