Relaxing music and ASMR triggers have their similarities and their differences.
Similarities include: both can induce relaxation, both have strong auditory component, and both can induce a type of chills or tingles.
Differences include: music is almost all auditory (vibrations can be another sensory input method), the type of chills induced are slightly different, and music may have a stronger emotional component.
And then there is the biggest difference of them all.