Great question. Their result in this area did surprise me. Conscious reflection on past negative memories slowly turns them into less negative and less painful memories. There is a lot of work here done by Pennebaker about how writing about past negative events transforms our memory of them [1]. And the work done by my lab started off with a system that facilitated these reflections through technology [2]. There is more recent work on this in press.
I think the difference lies in the structure. Rumination is symptomatic of depressive thinking and often characterized by intrusive negative thoughts. Reflection on the other hand is the conscious process of sitting down and reevaluating a past situation (often in writing).
1. Pennebaker, J. W., & Chung, C. K. (2011). Expressive writing: Connections to physical and mental health. In H. S. Friedman (Eds.), Oxford handbook of health psychology (pp. 417-437). Oxford, England: Oxford University Press.
2. Isaacs, E., Konrad, A., Walendowski, A., Lennig, T., Hollis, V., & Whittaker, S. (2013). Echoes from the past: how technology mediated reflection improves well-being (p. 1071). ACM Press. http://doi.org/10.1145/2470654.2466137