Are we talking about IRBM = Intermediate Range Ballistic Missile? If so then they are pretty much the same aside from their range.
Balistic Missile must be detected early after launch to counter, and that require satelite surveilance. For balistic missile the counter currently rather popular is "kinetic kill" interceptor or hit to kill type which designed to destroy target by physically slamming into it rather than traditional warhead, which require crazy precission. This is one of the reason why developed country invest technology hit it during its midcourse and not after because they know how low the possibility going to be. Satellite is definetly a must have in this type of engagement and we dont have any atm.
Hypersonic; off course each SAM system will claim able to take down heypersonic missiles but in reality the possibility is still low specially to counter the one that flying low. Seeing the missiles and able to lock on it are 2 different things, to see it coming the SAM def system need AWACS flying 24 hours a day simply because it cant see whats coming over the horizon. WIthout AWACS the best reponse time for the system to lock the target would be when it appear on the horizon, with that kind of speed it will reduce the response time. This is when the man behind the system, Firing protocol, beurocracy, system computation speed and type of missiles to be fired, etc will decide the outcome. And with Hypersonic missiles the chance to be able to fire the second missile if the first one miss is really low.
Yes everything has a counter weapon but to think it will effectively take the threat down with high possibility is against the reality, even with good IADS the possibility remain low to counter certain type of threat. This is why almost every major military naval excersice, missiles testing, there is often shadowed by their adversary (ship or aircraft) to gather telemetry , electronic intelligence from missile, radar signature, etc to have more information how to counter them. In the case of US they have RC-135S Cobra ball.