Two seemingly puzzling observations on two magnetic systems were analyzed. For the oxide -hydrides Sr2VO3H, Sr3V2O5H2, and SrVO2H, made up of VO4H2 octahedra, the spin orientations of the V3+ (d(2), S = 1) ions were reported to be different, namely, perpendicular to the H-V-H bond in Sr2VO3H but parallel to the H-V-H bond in Sr3V2O5H2 and SrVO2H, despite that the d-state split patterns of the VO4H2 octahedra are similar in the three oxide-hydrides. Another puzzling observation is the contrasting magnetic structures of Sr2CoO2Cu2Te2 and Sr2MnO2Cu1.58Te2, consisting of the layers made up of corner-sharing MO4Te2 (M = Co, Mn) octahedra. The Co2+ spins in each CoO2Te2 layer are antiferromagnetically coupled with spins perpendicular to the Te-Co-Te bond, whereas the Mn3+/Mn2+ ions of each MnO2Te2 layer are ferromagnetically coupled with spins parallel to the Te-Mn-Te bonds. We investigated the cause for these observations by performing firstprinciples density functional theory (DFT) calculations for stoichiometric phases Sr2VO3H, Sr3VO3H, SrVO2H, Sr2CoO2Cu2Te2, and Sr2MnO2Cu2Te2, as well as nonstoichiometric phase Sr2MnO2Cu1.5Te2. Our study reveals that the V3+ ions in all three oxide -hydrides should have the spin orientation parallel to the H-V-H bond. The unusual magnetic structure. of the MnO2Te2 layers of Sr2MnO2Cu1.52Te2 arises from the preference of a Mn3+ spin to be parallel to the Te-Mn-Te bond, the ferromagnetic spin exchange between adjacent Mn3+ and Mn2+ ions, and the nearly equal numbers of Mn3+ and Mn2+ ions in each MnO2Te2 layer. We show that the spin orientation of the magnetic ions in an antiferromagnetically coupled perovskite layer, expected in the absence of nonmagnetic ion vacancies, cannot be altered by the magnetic ions of higher oxidation that result from trace vacancies at the nonmagnetic ion sites.