We classify gamma-ray bursts (GRBs) according to their observed durations and physical properties of their spectra. We find that long/hard bursts (of duration T₉₀>2.5 s, and typical photon energy E_p0.8 MeV, corresponding to BATSE's energy fluence hardness H^e₃₂>3) show the strongest deviation from the three-dimensional Euclidean brightness distribution. The majority of GRBs, i.e., short bursts (T₉₀<2.5 s) and long/soft bursts (with T₉₀>2.5 s, and H^e₃₂<3), show little, if any, deviations from the Euclidean distribution. These results contradict the prediction of extragalactic GRB models that the most distant bursts should be the most affected by cosmological energy redshift and time dilation (long/soft GRBs). The strongly non-Euclidean GRB subclass has very hard spectra of typical photon energy above ~1 MeV, i.e., outside the ideal energy range for optimal detection by BATSE. Selection effects caused by BATSE inefficient triggering and/or intrinsic burst properties may cause the strong deviation from the Euclidean distribution for the hardest class of long GRBs. Our results imply strong luminosity and spectral evolution of GRB sources placed at extragalactic distances. Whether there coexist multiple GRB populations with different (Galactic or extragalactic) origins remains an open question.