Spin quantum beat spectroscopy is employed to investigate the in-plane anisotropy of the spin dynamics in (001) GaAs/AlGaAs quantum wells induced by an external electric field. This technique allows the anisotropy of the spin relaxation rate Γs and the electron Landé g factor g* to be measured simultaneously. The measurements are compared to similar data from (001) GaAs/AlGaAs quantum wells with applied shear strain and asymmetric barrier growth. All of these operations act to reduce the symmetry compared to that of a symmetric (001) quantum well in an identical manner (D2d → C2v). However, by looking at the anisotropy of both Γs and g* simultaneously we show that the microscopic actions of these symmetry breaking operations are very different. The experiments attest that although symmetry arguments are a very useful tool to identify the allowed spin dependent properties of a material system, only a microscopic approach reveals if allowed anisotropies will manifest. © 2013 American Physical Society.