What these findings suggest, the authors conclude, is that endurance training and weight training may have different physiological effects within the brain and cause improvements in different types of memory.
The NYTimes with research -- again, and again, and again -- on how exercise improves brain function.
Going for a run doesn't exactly equal an Alzheimer's-free brain (as this article details), but in fact aerobic exercise plus weight training gives you the best chance of not forgetting, well... everything.