Difference Between Lean Vs. Six Sigma

My company is actively deploying Lean Mfg principles.  To this point, we have not been heavily involved with Six Sigma.  Although recently our Customers have heightened our awareness of Six Sigma by asking/ requiring us to participate in their Six Sigma efforts - including becoming certified.

Side-by-Side there appears to be a relationship between Lean and Six Sigma.  But, I'm really not sure of the SPECIFIC differences/ benefits of each effort?    Which is why I'm posting this note.

I see Lean to be more Mfg/ Operations focused - although the principles can be applied across the company.  I see Six Sigma to be more focused on "white collar" processes, although it too can be applied across the company.  Six Sigma feels like the right approach.  It also feels like it NEEDS to co-exist with Lean; but, not replace Lean or vice versa.

Which approach is better?  Do you need both?  How should I respond to my management that want to know the hardline differences/ benefits?