What is the difference between "synergistic" and "synergetic"?

Other than synergistic having some specialized meanings in theology and medicine, both have the same definition as per the OED. Synergistic is the older of the two and, at least in my experience, more common.

Synergistic is older and is still used scientifically in many fields. It usually means that there is a proven result that is more than the sum of its parts. I would use this term if there are corroborating results. Synergetic is newer and is most often used in coaching for productivity in work groups. It usually implies the intent and determination to produce better outcomes working in synergy with others, regardless of success.