Do BLDC and Induction motors have the same efficiency vs. load relation?
The efficiency vs. load curves for any types of electric motors will be generally similar. When the motor is turning with no load, there are still some losses, but the output mechanical power is zero. Since zero output divided by any input is zero, the no-load efficiency is always zero. The effect of the no-load losses has some effect at all loads, but the effect varies as the large differences in efficiency below 20% of rated load for different motor ratings in your example curves shows. Since permanent magnet motors have no excitation losses, the no-load losses will probably be less, but not zero.

When comparing one type of motor with another, it important to consider the losses in the control system. If the control system is considered, the shape of the curves will be similar, but the overall efficiency will be lower for all types of motor.