In typical photoluminescence, emitters within an ensemble radiate independently, without correlations, whereas interactions between them can enable cooperative processes. Superfluorescence, where excited electric dipoles spontaneously couple coherently, and amplified spontaneous emission with an avalanche-like stimulated amplification of initially spontaneously emitted photons, can occur. Here, we present experiments in a thin film of giant CsPbBr3 perovskite nanocrystals where temperature and excitation density can drive transitions between both regimes. Below ~45 K, superfluorescence is observed, and above ~100 K, amplified spontaneous emission is found, with a transition region in-between. We dissect the signatures of the different collective effects, which can be quite similar and thereby present the risk of misinterpretation. Our results provide fundamental insights into cooperative emission phenomena that recently have become a focus with perovskite materials due to their potential applications as bright (quantum) light sources.