Hard sphere colloidal particles are a basic model system to study phase transitions, self-assembly and out-equilibrium states. Experimentally it has been shown that oscillatory shearing of a monodisperse hard sphere glass, produces two different crystal orientations; a face centered cubic (FCC) crystal with the close packed direction parallel to shear at high strains and an FCC crystal with the close packed direction perpendicular to shear at low strains. Here, using Brownian dynamics simulations of hard sphere particles, we have examined high volume fraction shear-induced crystals under oscillatory shear as well their glass counterparts at the same volume fraction. While particle displacements under shear in the glass are almost isotropic, the sheared FCC crystal structures oriented parallel to shear, are anisotropic due to the cooperative motion of velocity vorticity layers of particles sliding over each other. These sliding layers generally result in lower stresses and less overall particle displacements. Additionally, from the two crystal types, the perpendicular crystal exhibits less stresses and displacements at smaller strains, however at larger strains, the sliding layers of the parallel crystal are found to be more efficient in minimizing stresses and displacements, while the perpendicular crystal becomes unstable. The findings of this work suggest that the process of shear-induced ordering for a colloidal glass is facilitated by large out of cage displacements, which allow the system to explore the energy landscape and find the minima in energy, stresses and displacements by configuring particles into a crystal oriented parallel to shear. (C) 2016 Elsevier B.V. All rights reserved.