Halide perovskites are a promising optical gain medium with high tunability and simple solution synthesis. In this study, two gain regimes, namely, amplified spontaneous emission and random lasing, are demonstrated in the same MAPbBr₃ halide perovskite single crystal. For this, photoluminescence is measured at a temperature of 4 K with pulsed femtosecond pumping by UV light with an 80 MHz repetition rate. Random lasing is observed in areas of the sample where a random resonator is formed due to cracks and crystal imperfections. In more homogeneous regions of the sample, the dominant regime is amplified spontaneous emission. These two regimes are reliably distinguished by the line width, the mode structure, the growth of the intensity after the threshold, and the degree of polarization of the radiation. The spectral localization of the stimulated emission well below the bound exciton resonance raises a question concerning the origin of the emission in halide perovskite lasers.