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While the terminology is imprecise, ICMBs tend to go up in a big arc making them visible to radar well in advance of a strike, whereas “hypersonic” missiles fly close to the earth, effectively hiding behind its curvature.

Isn't the difference that hypersonic missiles are supposed to be able to cruise at such speeds, not "just" fall along a ballistic (or, for the newer models, ballistic-ish) trajectory with a bit of steering at certain points, but powered flight all the way, with the maneuverability and potential stealth that entails?

Yeah, any time somebody says "this thing goes Mach <number>" the first question should be "at what altitude?" and the second should be "for how long?".

An AR-15 fires a bullet at Mach 3. Low altitude, maybe a second or so before it's lost a lot of speed.

Perhaps I'm stupid, but I thought they were differentiated from classic missiles by actively diverging from a birds eye path at random during flight. Do ICBMs already do this?