Photon Bose-Einstein condensation and photon thermalisation have been largely studied with molecular gain media in optical cavities. However, their observation with semiconductors has remained elusive despite a large body of experimental results and very well established theoretical models. In this work, these models are used to build a new theoretical framework that enables revisiting lasing to compare with photon Bose-Einstein condensation in the driven-dissipative regime. The thermalisation figures of merit and the different experimental procedures to asses thermalization are discussed. Finally, the fluctuations of the system and their relation to the different regimes are explored.