Technically my understanding of terminology is that the branch predictor is responsible for determining which branch to take when speculative execution encounters a branch. Speculative execution is the thing that will invalidate work if the branch predictor was wrong.

Also my understanding based on reading this thread is that a conditional move is harder to speculate across because of the data dependency carried across iteration loops, preventing speculation. With a conditional branch, speculation can keep executing the next loop and most of the time the branch predictor will guess correctly how to execute the next iteration for this problem.