In this study, the chemical freeze-out of hadrons, including light- and strange-flavor particles and light nuclei, produced in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), was investigated. Using the Thermal-FIST thermodynamic statistical model, we analyzed various particle sets: those inclusive of light nuclei, those exclusive to light nuclei, and those solely comprising light nuclei. We determined the chemical freeze-out parameters at \(\sqrt{s_\text {NN}}=\) 7.7–200 GeV and four different centralities. A significant finding was the decrease in the chemical freeze-out temperature \(T_{\text {ch}}\) with light-nuclei inclusion, with an even more pronounced reduction when considering light-nuclei yields exclusively. This suggests that light-nuclei formation occurs at a later stage in the system’s evolution at RHIC energies. We present parameterized formulas that describe the energy dependence of \(T_{\text {ch}}\) and the baryon chemical potential \(\mu _\text {B}\) for three distinct particle sets in central Au+Au collisions at RHIC energies. Our results reveal at least three distinct \(T_{\text {ch}}\) at RHIC energies correspond to different freeze-out hypersurfaces: a light-flavor freeze-out temperature of \(T_\text {L}\) = 150.2±6 MeV, a strange-flavor freeze-out temperature \(T_\text {s}\) = 165.1±2.7 MeV, and a light-nuclei freeze-out temperature \(T_{\text {ln}}\) = 141.7±1.4 MeV. Notably, at the Large Hadron Collider (LHC) Pb+Pb 2.76 TeV, the expected lower freeze-out temperature for light nuclei was not observed; instead, the \(T_{\text {ch}}\) for light nuclei was found to be approximately 10 MeV higher than that for light-flavor hadrons.