Gas giants orbiting interior to the ice line are thought to have been displaced from their formation locations by processes that remain debated. Here we uncover several new metallicity trends, which together may indicate that two competing mechanisms deliver close-in giant planets: gentle disk migration, operating in environments with a range of metallicities, and violent planet-planet gravitational interactions, primarily triggered in metal-rich systems in which multiple giant planets can form. First, we show with 99.1% confidence that giant planets with semi-major axes between 0.1 and 1 AU orbiting metal-poor stars ([Fe/H]<0) are confined to lower eccentricities than those orbiting metal-rich stars. Second, we show with 93.3% confidence that eccentric proto-hot Jupiters undergoing tidal circularization primarily orbit metal-rich stars. Finally, we show that only metal-rich stars host a pile-up of hot Jupiters, helping account for the lack of such a pile-up in the overall Kepler sample. Migration caused by stellar perturbers (e.g. stellar Kozai) is unlikely to account for the trends. These trends further motivate follow-up theoretical work addressing which hot Jupiter migration theories can also produce the observed population of eccentric giant planets between 0.1 and 1 AU.