They both seem to cover similar topics, with similar techniques. I can't see any reason these should remain as seperate tags.
This has been suggested already. bit-twiddling is a proposed synonym of bit-manipulation, and currently has a score of 3. If one more person votes for that synonym, it will be approved and take effect.
Of course, I can't cast that last vote because I don't have the required score of 5 on the bit-manipulation tag. You'll have to find someone who is an expert on bit manipulation…