Meh.. to me when someone says twist it looks like this. Where one part (the bottom) is fixed or going in the opposite direction to the movement of the other, thus twisting around each other. Thus the shoulders twisting (which is essentially the upper body/waist). Don't twist the body would mean don't twist the upper body (twist movement from the shoulders down into obliques etc) and lower body.
And when someone says rotation it looks like this. Rotating around a specific fixed point, but that point can also be at the central axis. So either hip rotating like an open/close door, or with the pivot point in the middle. They're different.