As you said, my main question is "why a classical magnet behaves differently than a quantum mechanical one"; If a classical magnetic moment were in an external magnetic field, it becomes aligned with the magnetic field or would have a precession around the magnetic field (I also don't know the difference between these two as raised in my first post here) while the spin state would not change in an external magnetic field. For example, the state ##|S_x+,t_0>=1/\sqrt(2)|S_z+>+1/\sqrt(2)|S_z->## in the magnetic field ##\vec B=B_0 \hat z## changes as ##|S_x+; t>=exp(-i\alpha t) |S_x+,t_0>## which means that the spin state hasn't changed in the magnetic field.Your question is still extremely vague. Are you asking why a classical magnet behaves differently than a quantum mechanical one? Or are you asking why precession exists in the first place?
I believe the source of confusion of the OP is the angular momentum involved. Precession requires external torque and "large" angular momentum. For a macroscopic bar magnet the onboard angular momentum causing the magnetization is negligible. Not so for a proton.I still don't get the question. A classical magnetic moment doesn't behave so differently from the quantum one (at least in the sense of Ehrenfest's theorem).