I sat in a meeting today, and I listened to a senior manager discuss Lean Six Sigma, and I realized how few people genuinely understand the difference. The manager described them badly, and generally seems to have missed the point by setting up Lean and Six Sigma as completely separate and un-correlated processes, when they're actually completely complementary, and doing one without the other is generally going to lead to a bad result.
Lean is the process of removing waste from a process system - it means eliminating steps that are unnecessary, repetitive or provide limited value. The goal is to produce a speed/agility-optimized process that gets the maximum value for the least investment.
Six Sigma is the process of eliminating variance from a process. It causes you to do the same process (presumably the one that produces a good product) repeatably, thus eliminating defects from your process. The goal is to produce nearly perfect products every single time.
The difference is very much the distinction between efficiency ("doing things right") and effectiveness ("doing the right things"). You could create an extremely lean process by eliminating all of the compensating controls that provide you with a quality product, but that would be against your Six Sigma goals. You could have a very high-quality process by triple-checking every single step, but that would be against the goals of agility.
Lean and Six Sigma are complementary processes that achieve a balance between speed and perfection, keeping the parts of the process that maximally achieve quality and ONLY those parts.