We compute numerical solutions of the resistive Hall MHD equations corresponding to pairwise magnetic island coalescence. The simulation results can be organized according to the relative sizes of three length scales: the electron dissipation length, ℓe; the ion inertial length, di; and the island wavelength, λ. We identify three qualitatively distinct regimes of magnetic island coalescence: (1) the resistive MHD limit, di ≲ ℓe ≪ λ; (2) the whistler-mediated limit, ℓe ≪ di ≪ λ; and (3) the whistler-driven limit, ℓe ≪ λ ≲ di. In the resistive MHD limit, magnetic flux piles up outside thin current sheets between the islands. The upstream Alfv¿n speed increases with increasing Lundquist number, and the reconnection rate is insensitive to the Lundquist number. In the whistler-driven limit, the electron and ion bulk flows decouple on the island wavelength scale. Magnetic flux pileup does not occur, and the coalescence proceeds on a whistler timescale that is much shorter than the Alfv¿n time. In the whistler-mediated limit, electron and ion bulk flows decouple in spatially localized ion inertial sheets around the island separatrices. Flux pileup is reduced, and the upstream Alfv¿n speed approaches a nearly constant value as the Lundquist number is increased. The maximum reconnection rate in the whistler-mediated limit is comparable to that observed in the resitive MHD limit over the Lundquist number range 500 < Sλ < 10000.