Effective - producing the expected output or serving the intended purpose. It is about 'doing the right things' and achieving goals/targets
Efficient - performing in the most optimal manner. It is about 'doing things right' i.e. doing it in the least time or in a least expensive way. It may be the wrong thing but it could have been done optimally.
An application oriented question on the topic along with responses can be seen below. The best answer was provided by Nilesh Bhanushali on 3rd January 2017.