Ballistic missiles do travel ar hypersonic speed, but when people (namely the US military) use the term "hypersonic missile" or similar, they usually mean a weapon that can manoeuvre in-atmosphere at hypersonic speeds using aerodynamic lift. Some of the Iranian missiles used so far can make some sort of maneuvres at these speeds and in-atmosphere (during terminal flight) but cannot handle sustained flight.

Some of these may be fired from a ballistic missile, but when the warhead enters the atmosphere they glide to the target at hypersonic speeds, making evasive maneuvres and approaching their target unpredictably. You can also get hypersonic cruise missiles (an insanely fast shahed) or artillery shells (eg. a railgun).

These weapons are significant because they are much harder to detect (radar waves cannot curve around the Earth, so flying low lets you hide under the "radar horizon") and much harder to intercept (you cannot predict their path mathematically, and most current ABM systems need a few KM of altitude to maneuvre themselves).

On the downside, they're harder to design and produce, namely because they need more advanced targeting, avionics, and materials to withstand the heat from air resistance for longer. Communication with these weapons is also hard as they generate a field of plasma at their tips that interferes with radio waves. By cruising at lower altitudes, they're also in range of other air defense systems such as cannon fire. Shahed drones in Russia recently changed tactics to fly higher to avoid 50cal. fire from Ukrainian defenders.