We present detailed analysis of the global relativistic electron dynamics as measured by total radiation belt content (RBC) during coronal mass ejection (CME) and corotating interaction region (CIR)‐driven geomagnetic storms. Recent work has demonstrated that the response of the outer radiation belt is consistent and repeatable during geomagnetic storms. Here we build on this work to show that radiation belt dynamics can be divided into two sequential phases, which have different solar wind dependencies and which when analyzed separately reveal that the radiation belt responds more predictably than if the overall storm response is analyzed as a whole. In terms of RBC, in every storm we analyzed, a phase dominated by loss is followed by a phase dominated by acceleration. Analysis of the RBC during each of these phases demonstrates that they both respond coherently to solar wind and magnetospheric driving. However, the response is independent of whether the storm response is associated with either a CME or CIR. Our analysis shows that during the initial phase, radiation belt loss is organized by the location of the magnetopause and the strength of Dst and ultralow frequency wave power. During the second phase, radiation belt enhancements are well organized by the amplitude of ultralow frequency waves, the auroral electroject index, and solar wind energy input. Overall, our results demonstrate that storm time dynamics of the RBC is repeatable and well characterized by solar wind and geomagnetic driving, albeit with different dependencies during the two phases of a storm.