Thin current sheet structures with a thickness comparable to the ion gyro-radius have been inferred from spacecraft observations during substorms. This study presents two-dimensional hybrid and Hall-MHD simulations of current sheet thinning and reconnection that include electron pressure tensor effects. Results demonstrate that reconnection occurs due to the electron pressure tensor effects as the sheet is compressed by the application of an out-of-plane electric field on the lobe boundaries. Results from hybrid and Hall-MHD calculations for the current sheet thinning process are compared. During the thinning period, the out-of-plane ion velocity from the hybrid simulation shows an enhancement at the edge of the sheet and a reduction at the sheet center. As reconnection proceeds, it becomes peaked along the Earth-tail direction away from the X point. In contrast, the out-of-plane ion velocity from the Hall-MHD simulation remains peaked at the center of the simulation. The ion off-diagonal pressure tensor effects are considered as the cause of the differing particle-ion and fluid-ion dynamics. The dynamics of current sheet thinning and reconnection is also modeled using a new integrated approach in which Hall-MHD calculations are embedded inside an MHD simulation. It is shown that the embedded simulation can provide smooth transitions of plasma and field quantities between the two regions, and the small-scale physics in the compressed current sheet and in the near-X-point region are well represented.