Strontium titanate (${\mathrm{SrTiO}}_3$) is the quintessential material for oxide electronics. One of its hallmark features is the transition, driven by antiferrodistortive (AFD) lattice modes, from a cubic to a ferroelastic low-temperature phase. Here we investigate the evolution of the ferroelastic twin walls upon application of an electric field. Remarkably, we find that the dielectric anisotropy of tetragonal ${\mathrm{SrTiO}}_3$, rather than the intrinsic domain wall polarity, is the main driving force for the motion of the twins. Based on a combined first-principles and Landau-theory analysis, we show that such anisotropy is dominated by a trilinear coupling between the polarization, the AFD lattice tilts, and a previously overlooked antiferroelectric (AFE) mode. We identify the latter AFE phonon with the so-called “$R$ mode” at $\sim 440{\mathrm{cm}}^{-1}$, which was previously detected in IR experiments, but whose microscopic nature was unknown.