Despite the ubiquity of thermal convection in nature and artificial systems, we still lack a unified formulation that integrates the system's geometry, fluid properties, and thermal forcing to characterize the transition from free to confined convective regimes. The latter is broadly relevant to understanding how convection transports energy and drives mixing across a wide range of environments, such as planetary atmospheres/oceans and hydrothermal flows through fractures, as well as engineering heatsinks and microfluidics for the control of mass and heat fluxes. Performing laboratory experiments in Hele-Shaw geometries, we find multiple transitions that are identified as remarkable shifts in flow structures and heat transport scaling, underpinning previous numerical studies. To unveil the mechanisms of the geometrically controlled transition, we focus on the smallest structure of convection, posing the following question: How free is a thermal plume in a closed system? We address this problem by proposing the degree of confinement A -the ratio of the thermal plume's thickness in an unbounded domain to the lateral extent of the system-as a universal metric encapsulating all the physical parameters. Here, we characterize four convective regimes different in flow dimensionality and time dependency and demonstrate that the transitions across the regimes are well tied with A . The introduced metric A offers a unified characterization of convection in closed systems from the plume's standpoint.