Growth shapes of Ag islands formed on Ag(111) during submonolayer deposition at different temperatures were studied with scanning tunneling microscopy, and analyzed via kinetic Monte Carlo simulation of a suitable atomistic lattice-gas model. Distinct shape transitions can be observed, from dendrites with triangular envelopes at low temperatures (below 140 K) to more isotropic fat fractal islands at intermediate temperatures, and then to distorted hexagonal shapes with longer Bsteps and shorter A steps at higher temperatures (above 170 K). In contrast, the equilibrium island shapes in this system are almost perfect hexagons displaying a near-sixfold symmetry. Modeling reveals that the broken symmetry of growth shapes at low and high temperatures derives from the interplay of diffusion-mediated aggregation with different aspects of a corner diffusion anisotropy. The broken symmetry is less clear at intermediate temperatures, where the near-isotropic fractal shapes reflect in part a kink Ehrlich-Schwoebel effect.