Detailed extended oscillating features above the Cu M2,3VV Auger transition, recently named EXFAS (Extended Fine Auger Structure), and above the Cu M2,3 core edge, named EELFS (Electron Energy-Loss Fine Structure), on the polycrystalline Cu surface have been compared to assess the short-range nature of the EXFAS features. To obtain the structural information in terms of Debye-Waller factor, interatomic distance, anharmonic effects, backscattering amplitude, and phase-shift functions, the data analysis has been performed following the EXAFS (Extended X-ray Absorption Fine Structure) procedure. The intensity of the extended structures decreases strongly when the temperature increases. In both cases no difference, as a function of temperature, in the nearest-neighbor distance was observed but a sizeable increase of the Debye-Waller factor was observed. The Debye-Waller factor has been fitted, as a function of temperature, to obtain the Debye temperature. The main result shows that the EELFS spectroscopy mainly investigates the bulk properties because of the high mean free path of the analyzed electrons. On the contrary, the Debye-Waller factor obtained from the analysis on the EXFAS structures, which are due to the first 2–4 atomic layers, is greater than that obtained from the EELFS analysis because of the greater movement of the surface atoms with respect to the bulk atoms. The close analogy between the EELFS and EXFAS structural results confirms that the extended features above the Auger transition are dominated by a genuine autoionization effect rather than by a diffraction process and/or a density-of-state effects which modulate the background of the secondary emitted electrons. Our interpretation is confirmed by the complete lack of the extended Auger features in the electron yield spectrum, N(E), when a monochromatic X-ray source is used.