Recently, amorphous oxide semiconductors have gained significant interest due to their low-temperature processability, high mobility, and high areal uniformity for display backplanes and other large area applications. A multication amorphous oxide, amorphous indium gallium zinc oxide (a-IGZO), has been extensively researched and is now being used in commercial applications. It has been proposed that, in a-IGZO semiconductors, overlapping In-5s orbitals form the conduction path and the carrier mobility is limited due to the presence of multiple cations, which creates a potential barrier for the electronic transport. A multianion approach toward amorphous semiconductors has been suggested to overcome this limitation, and has been shown to achieve Hall mobilities up to an order of magnitude higher compared to multication amorphous semiconductors. In the present work, we compare the electronic structure and electronic transport in a multication amorphous semiconductor, a-IGZO, and a multianion amorphous semiconductor, amorphous zinc oxynitride (a-ZnON) using computational methods. Our results show that, in a-IGZO, the carrier transport path is through the overlap of outer s-orbitals of mixed cations, whereas, in a-ZnON, the transport path is through the overlapping Zn-4s orbitals, which is the only type of metal cation present. We also show that for multicomponent ionic amorphous semiconductors, the electron transport can be explained in terms of the orbital overlap integral, which can be calculated simply from the structural information. The orbital overlap integral has a direct correlation with the carrier effective mass, which is calculated using computationally expensive first-principles density functional theory based methods.