4 Dogs,
In both the wings level and the slight bank towards live engine cases the lateral forces are in balance. With the nose yawed just enough towards the live engine the aircraft will sidelsip down its original track. Its lateral stability will cause it to try to roll away from this, but this can be prevented by using the ailerons to hold the wings. In this situation the aircarft down-track sideslip will increase until all forces are in balance. The ball will then be central indicating zero slip. But the aircraft will be in a constant velocity sideslip down the track.
If on the other hand, the rudder is used to hold the nose on the original heading, the rudder force will cause sideslip away from the live engine. This is usually balanced by banking slightly towards the live engine. This tilts the lift force so that rudder force and horizontal lift component are equal. In this situation the ball will be out towards the live engine but the aircraft will not be slipping.
So in both cases the lateral forces are balanced. In one there is sideslip while in the other there is not. If you interpret the ball as indicating sideslip, it tells lies in both cases. But if you interpret the ball as telling you whether lateral forces are in balance, it tells lies in the slight bank case only.