Amorphous zinc tin oxides (a-ZTO), which are stoichiometrically close to the Zn$2$SnO$4$ and ZnSnO$3$ phases, have been deposited using remote-plasma reactive sputtering, and incorporated as the channel layers in thin film transistors (TFTs). The influence of tin composition and annealing temperatures on the structural and phase evolutions of the thin films, and the electrical performances of the TFTs are investigated. Zn$2$SnO$4$ exhibited randomly oriented polycrystalline peaks at annealing temperatures ≥700 °C, while ZnSnO$3$ decomposed into Zn$2$SnO$4$ and SnO$2$ at 950 °C. TFTs employing a Zn$2$SnO$4$ channel, after a post-deposition annealing at 500 °C, exhibited a field effect mobility ~14 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ and a sub-threshold slope ~0.6 V dec$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. When the tin content was increased in the channel, as in ZnSnO$3$, TFTs exhibited an increase in field effect mobility ~20 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, but with a slight deterioration of sub-threshold slope to ~0.8 V dec$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. When the post-deposition annealing temperature was reduced to 300 °C, a mobility as high as ~10 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ was still achieved, however, a significant shoulder in the IDS–VGS curve, together with a higher off-state current was observed. TFT characteristics are explained by the sub-bandgap defect states measured by photothermal deflection spectroscopy and the extracted Urbach energies.