The simple solution processability at room temperature exposes lead halide perovskite semiconductors to a non-negligible level of unintentional structural and chemical defects. Ascertained that their primary optoelectronic properties meet the requirement for high efficiency optoelectronic technologies, a lack of knowledge about the nature of defects and their role in the device operation currently is a major challenge for their market-scale application due to the issues with stability and reliability. Here, we use excitation correlation photoluminescence (ECPL) spectroscopy to investigate the recombination dynamics of the photogenerated carriers in lead bromide perovskites and quantitatively describe the carrier trapping dynamics within a generalization of the Shockley-Read-Hall formalism. The superior sensitivity of our spectroscopic tool to the many-body interactions enables us to identify the energetics of the defects. In fact, in the case of polycrystalline films, depending on the synthetic route, we demonstrate the presence of both deep and shallow carrier traps. The shallow defects, which are situated at about 20 meV below the conduction band, dope the semiconductor, leading to a substantial enhancement of the photoluminescence quantum yield despite carrier trapping. At excitation densities relevant for lasing, we observe breakdown of the rate-equation model, indicating a buildup of a highly correlated regime of the photocarrier population that suppresses the nonradiative Auger recombination. Furthermore, we demonstrate that colloidal nanocrystals represent virtually defect-free systems, suffering from nonradiative quenching only due to subpicosecond Auger-like interactions at high excitation density. By correlating the fabrication conditions to the nonradiative loss channels, this work provides guidelines for material engineering towards superior optoelectronic devices.