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
To the scientific mind, mindfulness might seem hokey. I certainly thought so for years until I saw it promoted on HN with some scientific research backing its efficacy. Then I tried it and was impressed with the results.
For a constant ruminator like me, learning to properly reflect has improved my life more than almost anything else.
I came to realize that I either suffered from intrusive thoughts that remained vague, oppressive, and kept returning in full-force, or I pushed the thoughts away by constant reading, activity, or various intoxicants.
But if I sat down and wrote unfiltered, or just more actively allowed myself to 'fully' observe the situation including the thoughts and emotions that came along, they would often start to untangle by themselves. Not always, but often enough that it really made me a happier person.
There are things that don't untangle themselves, and for that I'm seeing a therapist. But they're doing basically the same kind of thing (CBT-based therapy).