For aircraft speeds which are much greater than the speed of sound, the aircraft is said to be hypersonic. Typical speeds for hypersonic aircraft are greater than 3000 mph and Mach number M greater than five, M > 5. We are going to define a high hypersonic regime at M > 10 to account for re-entry aerodynamics.
Supersonic means faster than the speed of sound, while hypersonic means specifically five times faster than the speed of sound. Therefore, all hypersonic speeds are also supersonic, but something supersonic is not necessarily hypersonic.