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In this paper, a relaxation magnetohydrodynamic model is used to study magnetic reconnection phenomena in pulsed-power-driven Z-pinch inverse wire arrays. We focus on certain characteristics of two distinct modes that differ by resistivity. A magnetic field alignment that is both anti-parallel and open is created in high-resistivity mode. This produces a pronounced slow/standing shock wave and outflows can be accelerated to super-magnetosonic velocities. In low-resistivity mode, the entire magnetic field is closed and there is no pronounced slow/standing shock wave. The outflow velocity along the neutral line is accelerated to magnetosonic velocities between the two magnetic islands, but slows afterwards. It is difficult to achieve steady or quasi-steady magnetic reconnection in pulsed-power-driven Z-pinch inverse wire arrays.