Electrons in a non-thermal distribution can influence the electronic transport properties of metals with weak electron-phonon coupling. Relaxation processes involving non-thermal electrons competing with the thermalized electron system has led to inconsistencies in the understanding of how electrons scatter and relax with the less energetic lattice. Recent theoretical and computational works have shown that the rate of energy relaxation with the metallic lattice will change depending on the thermalization state of the electrons. Even though 20 years of experimental works have focused on understanding and isolating these electronic relaxation mechanisms with short-pulsed irradiation, discrepancies between these existing works have not clearly answered the fundamental question of the competing effects between non-thermal and thermal electrons losing energy to the lattice. In this work, we demonstrate the ability to measure the electron relaxation for varying degrees of both electron-electron and electron-phonon thermalization. This series of measurements of electronic relaxation over a predicted effective electron temperature range up to ~3,500 K and minimum lattice temperatures of 77 K validate recent computational and theoretical works that theorize how a nonequilibrium distribution of electrons transfers energy to the lattice. Utilizing this wide temperature range during pump-probe measurements of electron-phonon relaxation, we explain the discrepancies in the past two decades of literature of electronic relaxation rates. We experimentally demonstrate that the electron-phonon coupling factor in gold increases with increasing lattice temperature and laser fluences. Specifically, we show that at low laser fluences corresponding to small electron perturbations, energy re- laxation between electrons and phonons is mainly governed by non-thermal electrons and at higher laser fluences, non-thermal electron scattering with the lattice can still influence the energy relaxation mechanisms. We also study the effects of an adhesion layer between thin gold films and nonmetal substrates on electron-phonon coupling by repeating the measurements for a Au/Ti/Si system. We observe that the coupling between the electronic and the vibrational states is increased by more than five fold with the inclusion of a ~2 nm Ti adhesion layer that strengthens the interfacial bonding.