Efficiency is output energy divided by input energy to give you an idea of how much value for your investment you are getting. We use this mostly with heating and cooling systems.
Efficacy is defined as the ability to produce a desired result. Efficacy is when you put energy in and get something else out. For example, if you are putting energy into a ceiling fan, you will get air flow out. The same goes for lighting where you put energy in and get Lumens out.