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Magnetic reconnection in partially ionized plasmas is a ubiquitous and important phenomenon in both laboratory and astrophysical systems. Here, simulations of partially ionized magnetic reconnection with well-matched initial conditions are performed using both multi-fluid and fully-kinetic approaches. Despite similar initial conditions, the time-dependent evolution differs between the two models. In multi-fluid models, the reconnection rate locally obeys either a decoupled Sweet–Parker scaling, where neutrals are unimportant, or a fully coupled Sweet–Parker scaling, where neutrals and ions are strongly coupled, depending on the resistivity. In contrast, kinetic models show a faster reconnection rate that is proportional to the fully-coupled, bulk Alfvén speed, vA⋆. These differences are interpreted as the result of operating in different collisional regimes. Multi-fluid simulations are found to maintain νniL/vA⋆≳1, where νni is the neutral–ion collision frequency and L is the time-dependent current sheet half-length. This strongly couples neutrals to the reconnection outflow, while kinetic simulations evolve to allow νniL/vA⋆<1, decoupling neutrals from the reconnection outflow. Differences in the way reconnection is triggered may explain these discrepancies.