Controlling grain orientations within polycrystalline all-inorganic halide perovskite solar cells can help increase conversion efficiencies toward their thermodynamic limits, however the forces governing texture formation are ambiguous. Using synchrotron X-ray diffraction, we report meso-structure formation within polycrystalline CsPbI2.85Br0.15 powders as they cool from a high-temperature cubic perovskite (α-phase). Tetragonal distortions (β-phase) trigger preferential crystallographic alignment within polycrystalline ensembles, a feature we suggest is coordinated across multiple neighboring grains via interfacial forces that select for certain lattice distortions over others. External anisotropy is then imposed on polycrystalline thin films of orthorhombic (γ-phase) CsPbI3-xBrx perovskite via substrate clamping, revealing two fundamental uniaxial texture formations; (i) I-rich films possess orthorhombic-like texture (<100> out-of-plane; <010> and <001> in-plane), while (ii) Br-rich films form tetragonal-like texture (<110> out-of-plane; <1-10> and <001> in-plane). In contrast to relatively uninfluential factors like the choice of substrate, film thickness and annealing temperature, Br incorporation modifies the γ-CsPbI3-xBrx crystal structure by reducing the orthorhombic lattice distortion (making it more tetragonal-like) and governs the formation of the different, energetically favored textures within polycrystalline thin films.