Heme-regulated inhibitor (HRI) is one of the four mammalian kinases that phosphorylate eIF2α, facilitating a cellular response to stress through the regulation of mRNA translation. Originally identified as a heme sensor in erythroid progenitor cells, HRI has since emerged as a potential therapeutic target in both cancer and neurodegeneration. Here, we characterise two modes of HRI inhibition using structural mass spectrometry, biochemistry, and biophysics. We examined several competitive ATP-mimetic inhibitors - dabrafenib, encorafenib, and GCN2iB - and compared them with the heme-mimetic allosteric inhibitor, hemin. By combining hydrogen-deuterium exchange mass spectrometry with protein models generated by AlphaFold 3, we investigated the structural basis of inhibition by dabrafenib and hemin. Our analysis revealed that hemin inhibition induces large-scale structural rearrangements in HRI, which are not observed with ATP-mimetic inhibitors. Our results suggest that HRI may be inhibited using two distinctly different modalities, which may guide future drug development.