Energy storage and generalized energy storage (GES) such as electric vehicles (EVs) and heating, ventilation, and air conditioning (HVAC) systems play a critical role in enhancing the flexibility of power systems. The shared system architecture can improve utilization rates of energy storage and reduce configuration costs. However, the heterogeneity and inherent uncertainty of GES pose significant challenges to the rational configuration and operation of energy storage. To address this, we employ a two-stage distributionally robust capacity configuration method for shared energy storage considering the flexibility and uncertainty of distributed resources. First, by integrating the operational characteristics of both physical and virtual energy storage, a shared system architecture is proposed for the GES. Second, to overcome the limitation of existing EV aggregation models, which are typically tailored for ideal battery behaviors, a more accurate aggregation model is introduced based on the parameter planning, termed the GES model. An uncertainty probability set modeling approach for demand-side resources is derived based on this model. Finally, considering the flexibility and uncertainty associated with EVs and HVAC systems, a distributionally robust optimization model for shared energy storage capacity configuration is proposed. Simulation results demonstrate that the proposed method increases the revenue of operators and the utilization of energy storage resources, while also reducing the configuration capacity.