(I came across the following write-up on a discussion thread in one of the testing forums and am posting it here. Unfortunately, I forgot the name of the original contributor of the following piece)
The primary difference:Efficiency - productivity metric and Effectiveness - quality metric!
Efficiency is a productivity metrics meaning how fast one can do something. Hence Testing efficiency metric can be "No. of test cases executed per hour or per person day". This explains how efficient (i.e. fast) the person is at testing.
Effectiveness is a quality metrics meaning how good a person is at testing. Hence Testing effectiveness metrics can be "No. of bugs identified by a tester in a given feature / Total no. of bugs identified in that feature". Here the difference between total bugs and bugs identified by the tester could be that some bugs must have been uncovered by the customer since the tester was not able to detect them during testing.
If bugs uncovered by a tester and total no. of bugs are same, meaning that all the defects were uncovered by the tester, then he is 100 % effective in testing the product.