The seminal paper by Zhirnov (1958 Zh. Eksp. Teor. Fiz. 35 1175-80) explained why the structure of domain walls in ferroelectrics and ferromagnets is drastically different. Here we show that the antiparallel ferroelectric walls in rhombohedral ferroelectric BaTiO(3) can be switched between the Ising-like state (typical for ferroelectrics) and a Bloch-like state (unusual for ferroelectric walls but typical for magnetic ones). Phase-field simulations using a Ginzburg-Landau-Devonshire model suggest that this symmetry-breaking transition can be induced by a compressive epitaxial stress. The strain-tunable chiral properties of these domain walls promise a range of novel phenomena in epitaxial ferroelectric thin films.