If our ultimate goal is to achieve something and make a difference (in people's lives), then we can say that we are effective when we achieve that goal. So, effectiveness is about achieving a goal and making a difference (doing the right thing).
Efficiency, on the other hand, is about doing things the best way possible. It is a measure of how well we did a specific task or performed an assignment (doing it right).
We may be very efficient in doing something, but if the ultimate result is meaningless, then we have not been effective. However, to be effective, we may need to improve certain processes (make them more efficient).
We can argue that the reason why we may want to be efficient in the first place, is to make us more effective. Efficiency for efficiency's sake is pointless. So, aim for effectiveness in all that you do. Efficiency will follow.
Do the right thing!