Stress generated during deposition or annealing of thin films is a main factor determining the formed crystal phases and influences the lattice strain of the polar orthorhombic phase. It is difficult to discriminate between stress and strain effects on polycrystalline ferroelectric HfO₂ films, and the direct impact of orthorhombic lattice strain on ferroelectric polarization has yet to be determined experimentally. Here, we analyze the crystalline phases and lattice strain of several series of doped HfO₂ epitaxial films. We conclude that stress has a critical influence on metastable orthorhombic phase stabilization and ferroelectric polarization. On the contrary, the lattice deformation effects are much smaller than those caused by variations in the orthorhombic phase content. The experimental results are confirmed by density functional theory calculations on HfO₂ and Hf_0.5Zr_0.5O₂ ferroelectric phases.