"Efficacy" is not a commonly-used word. It means that something is able to produce the intended effect, to do what it is you want, to get the job done.
"Efficiency" is being able to do something with the least amount of effort or waste.
An Abrams tank, my Kia crossover SUV and a motorbike would all be efficacious in getting me from my home to work. But there would be varying degrees of efficiency involved in the three, in terms of cost and fuel use.
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