Amorphous metal oxides are central to a variety of technological applications. In particular, indium gallium oxide has garnered attention as a thin-film transistor channel layer material. In this work we examine the structural evolution of indium gallium oxide gel-derived powders and thin films using infrared vibrational spectroscopy, X-ray diffraction, and pair distribution function (PDF) analysis of X-ray total scattering from standard and normal incidence thin-film geometries (tfPDF). We find that the gel-derived powders and films from the same aqueous precursor evolve differently with temperature, forming mixtures of Ga-substituted In₂O₃ and In-substituted β-Ga₂O₃ with different degrees of substitution. X-ray total scattering and PDF analysis indicate that the majority phase for both the powders and films is an amorphous/nanocrystalline β-Ga₂O₃ phase, with a minor constituent of In₂O₃ with significantly larger coherence lengths. This amorphous β-Ga₂O₃ phase could not be identified using the conventional Bragg diffraction techniques traditionally used to study crystalline metal oxide thin films. The combination of Bragg diffraction and tfPDF provides a much more complete description of film composition and structure, which can be used to detail the effect of processing conditions and structure-property relationships. This study also demonstrates how structural features of amorphous materials, traditionally difficult to characterize by standard diffraction, can be elucidated using tfPDF.