A number of methods proposed in the past few years have been aimed at accelerating the sampling of rare events in molecular dynamics simulations. We recently introduced a method called Boxed Molecular Dynamics (BXD) for accelerating the calculation of thermodynamics and kinetics (J. Phys. Chem. B 2009, 113, 16603-16611). BXD relies upon confining the system in a series of adjacent "boxes" by inverting the projection of the system velocities along the reaction coordinate. The potential of mean force along the reaction coordinate is obtained from the mean first passage times (MFPTs) for exchange between neighboring boxes, simultaneously providing both kinetics and thermodynamics. In this paper, we investigate BXD in the context of its natural relation to a kinetic master equation and show that the BXD first passage times (FPTs) include different time scales-a fast short time decay due to correlated dynamical motion and slower long time decay arising from phase space diffusion. Correcting the FPTs to remove the fast correlated motion yields accurate thermodynamics and master equation kinetics. We also discuss interrelations between BXD and a recently described Markovian milestoning technique and use a simple application to show that, despite each method producing distinct nonstatistical effects on time scales on the order of dynamical decorrelation, both yield similar long-time kinetics.