Using a multi-code approach, we investigate current sheet thinning and the onset and progress of fast magnetic reconnection, initiated by temporally limited, spatially varying, inflow of magnetic flux. The present study extends an earlier collaborative effort into the transition regime from thick to thin current sheets. Again we find that full particle, hybrid, and Hall-MHD simulations lead to the same fast reconnection rates, apparently independent of the dissipation mechanism. The reconnection rate in MHD simulations is considerably larger than in the earlier study, although still somewhat smaller than in the particle simulations. All simulations lead to surprisingly similar final states, despite differences in energy transfer and dissipation. These states are contrasted with equilibrium models derived for the same boundary perturbations. The similarity of the final states indicates that entropy conservation is satisfied similarly in fluid and kinetic approaches and that Joule dissipation plays only a minor role in the energy transfer.