This question comes up a lot. A good metaphor to illustrate the difference is the one of cleaning the floor with a toothbrush. It's effective, in that it achieves its purpose and you get a nice clean floor. However, it is not a very efficient method, as it takes forever, gives you a sore back and knees and probably ruins the toothbrush. Effectiveness is about having the desired effect; efficiency is about efficient use of resources.

Effectiveness is a narrow term as it include doing the work in a effective way but efficiency is a wider term than effectiveness it means doing the work in optimal time. Efficient work is good were we Concentrate in the quality of good😃😃and effective work is good were we concentrate on quantity of product (to produce a standard output in a standard time)

To answer the second part of your question, it is hard to see how that could possibly be true. If you work efficiently, then it should be effective (and achieve the results you would like).