Geological heterogeneities affect the dynamics of carbon dioxide (CO2) plumes in subsurface environments in important ways. Previously, we showed how the dynamics of CO2 plumes are influenced by the multiscaled sedimentary architecture in deep brine fluvial-type reservoirs. The results confirm that representing small-scale features and the corresponding heterogeneity in saturation functions, along with hysteresis in saturation functions, are all critical to understanding capillary trapping processes. Here, we show that when heterogeneity and hysteresis are represented, the two conventional approaches for defining saturation functions, Brooks-Corey and van Genuchten, represent fundamentally different physical systems. The Brooks-Corey approach represents heterogeneity in entry pressures, and leads to trapping by capillary pinning. The van Genuchten approach represents a network of pores transporting the nonwetting fluid, across rock types, with negligible capillary entry pressure, and leads to capillary retardation. These differences significantly affect the large-scale characteristics of CO2 plumes (i.e., their mass, shape, and position).