This study investigates the applicability of different cavitation number definitions and the influence of Venturi geometry on cavitating flow dynamics within a narrow rectangular Venturi tube. Experiments were conducted in a closed-loop water tunnel using high-speed imaging and grayscale-based image processing to characterize cavity morphology and shedding behavior. Three kinds of cavitation numbers were evaluated. The results demonstrate that the inlet cavitation number fails to reflect cavitation intensity due to strong blockage effects, while the outlet cavitation number captures overall growth trends but lacks sensitivity to transitions in shedding mechanisms. In contrast, the pressure-drop cavitation number provides accurate and robust characterization of cavitation intensity and effectively identifies regime transitions between reentrant-jet- and shock-wave-dominated shedding. Geometric effects were also examined: larger divergence angles promote periodic large-scale cloud cavitation shedding due to stronger adverse pressure gradients, while smaller angles lead to quasi-steady cavitation with tail-dominated collapse. Furthermore, reducing throat height increased cavity length by weakening reentrant jet penetration. These findings provide new insights into the appropriate scaling of cavitation number in confined Venturi flows and advance the understanding of geometry-induced modulation of unsteady cavitation dynamics.