Biaxial strain is known to induce ferroelectricity in thin films of nominally nonferroelectric materials such as SrTiO3. By a direct comparison of the strained and strain-free SrTiO3 films using dielectric, ferroelectric, Raman, nonlinear optical and nanoscale piezoelectric property measurements, we conclude that all SrTiO3 films and bulk crystals are relaxor ferroelectrics, and the role of strain is to stabilize longer-range correlation of preexisting nanopolar regions, likely originating from minute amounts of unintentional Sr deficiency in nominally stoichiometric samples. These findings highlight the sensitive role of stoichiometry when exploring strain and epitaxy-induced electronic phenomena in oxide films, heterostructures, and interfaces.