Hi Michael,
I think that you're keying in on the word "sigma" and that it is perhaps the cause of some confusion.
Generally when you hear "Six Simga" mentioned, it is as Cornelius says -- it is a quality managmenet methodology. Think of it as just one more method in a family of quality managment approaches over they years. Other examples would be TQM (Total Quality Management), or ZD (Zero Defects).
The idea behind Six Sigma is that they wanted to drive their defect rate down to near zero. The goal was to achieve a rate of approximagtely one defect per million items. If you look at a normal distribution (a bell curve), to achieve a probability at such a low level you need to go approximately six standard deviations away from the mean. That is where the name Six Sigma comes from. It's just a shorthand way of referencing their goal of defects being at a rate comparable with one in a million.
WIth respect to the PERT task duration, the beta distribution version of the formula basically is taking your date estimates and forcing them onto a simple probability function that looks like a bell curve.
The beta distribution PERT formula is: duration = (optimistic + pessimitic + 4*most likely) / 6
When using this simple model, the standard deviation (sigma) is equal to (optimistic - pessimistic) / 6.
You'll need to look at the context to know whether they're talking about the quality methodology or whether they are actually referencing six standard deviations away from the mean. However, if they intend the quality methodology then Six Sigma is generally capitalized.
With respect to your specific question, I'm afraid that I'm unable to speak to the details without seeing the details of the question. However, I hope that the above discussion helps you understand Six Sigma vs. PERT.