Measurements of intrinsic alignments of galaxy shapes with the large-scale density field, and the inferred intrinsic alignments model parameters, are sensitive to the shape measurement methods used. In this paper we measure the intrinsic alignments of the Sloan Digital Sky Survey-III (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) LOWZ galaxies using three different shape measurement methods (reGaussianization, isophotal, and de Vaucouleurs), identifying a variation in the inferred intrinsic alignments amplitude at the 40% level between these methods, independent of the galaxy luminosity or other properties. We also carry out a suite of systematics tests on the shapes and their two-point correlation functions, identifying a pronounced contribution from additive PSF systematics in the de Vaucouleurs shapes. Since different methods measure galaxy shapes at different effective radii, the trends we identify in the intrinsic alignments amplitude are consistent with the interpretation that the outer regions of galaxy shapes are more responsive to tidal fields, resulting in isophote twisting and stronger alignments for isophotal shapes. We observe environment dependence of ellipticity, with brightest galaxies in groups being rounder on average compared to satellite and field galaxies. We also study the anisotropy in intrinsic alignments measurements introduced by projected shapes, finding effects consistent with predictions of the nonlinear alignment model and hydrodynamic simulations. The large variations seen using the different shape measurement methods have important implications for intrinsic alignments forecasting and mitigation with future surveys.