The two words are close, but not quite the same.
'Effective' means basically achieving or causing a desired result.
'Efficient' means that you do something with the least amount of effort required and/or it is well organized.
If some method is effective, we usually assume that it is efficient, but it may not be. It may have taken more effort than necessary, but still achieved the desired result.
Likewise, I can be very well organized, but not able to achieve my end result. If I run a political campaign, I can run an efficient one, but if my candidate loses the election, it is not effective.