Amorphous films and coatings are rapidly growing in importance. Yet, there is a dearth of high-quality structural data on sub-micron films. Not understanding how these materials assemble at atomic scale limits fundamental insights needed to improve their performance. Here, we use grazing-incidence x-ray total scattering measurements to examine the atomic structure of the top 50-100 nm of Ta2O5 films; mirror coatings that show high promise to significantly improve the sensitivity of the next generation of gravitational-wave detectors. Our measurements show noticeable changes well into medium range, not only between crystalline and amorphous, but also between as-deposited, annealed and doped amorphous films. It is a further challenge to quickly translate the structural information into insights into mechanisms of packing and disorder. Here, we illustrate a modeling approach that allows translation of observed structural features to a physically intuitive packing of a primary structural unit based on a kinked Ta-O-Ta backbone. Our modeling illustrates how Ta-O-Ta units link to form longer 1D chains and even 2D ribbons, and how doping and annealing influences formation of 2D order. We also find that all the amorphousTa2O5 films studied in here are not just poorly crystalline but appear to lack true 3D order.