Star rating of electrical appliances like AC / fridge
The star rating is a method of comparing energy usage of similar appliances over some period of time like a billing cycle or a year. That is related to efficiency, but not the same thing. For a fridge, the motor efficiency would be one important factor and the coefficient of performance of the refrigeration system would be another. Those are both related to energy used for cooling. Just as important is the thermal insulation and sealing of the door which prevent heat from entering the fridge from the outside. Those factors can be analyzed using engineering methods. For evaluation, an assumption needs to be made about how often the door is opened and how long it remains open. An assumption also need to be made about things being put in the fridge that are initially warmer than the internal temperature. That assumption would need to be equivalent for all products evaluated, but individual people are likely to use the product differently and experience different results.

The electrical and electronic control design may influence the efficiency of some appliances, but the motor design and the non-electrical aspects of the design are likely to be the most important factors.