APbBr3 (A = Cs, CH3NH3) are prototype halide perovskites having bandgaps of 2.30-2.35 eV at room temperature, rendering their apparent color nearly identical (bright orange but opaque). Upon optical excitation, they emit bright photoluminescence (PL) arising from carrier recombination whose spectral features are also similar. At 10 K, however, the apparent color of CsPbBr3 becomes transparent yellow, whereas that of CH3NH3PbBr3 does not change significantly due to the presence of an indirect Rashba gap. With increasing the excitation level, evolution of the PL spectra, which are excitonic at 10 K, reveals the emergence of P-band emission arising from inelastic exciton-exciton scattering. Based on the spectral location of the P-band, exciton binding energies are determined to be 21.6 +/- 2.0 and 38.3 +/- 3.0 meV for CsPbBr3 and CH3NH3PbBr3, respectively. Intriguingly, upon further increase in the exciton density, electron-hole plasma appears in CsPbBr3 as evidenced by both red-shift and broadening of the PL. This phase, however, does not occur in CH3NH3PbBr3 presumably due to polaronic effects. Although the A-site cation is believed not to directly impact optical properties of APbBr(3), our results underscore its critical role, which destines different high-density phases and apparent color at low temperatures.