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Photon Bose-Einstein condensation and photon thermalisation have been largelystudied with molecular gain media in optical cavities. Their observation withsemiconductors has remained elusive despite a large body of experimentalresults and a very well established theoretical framework. We use thistheoretical framework as a convenient platform to revisit photon Bose-Einsteincondensation in the driven-dissipative regime and compare with the lasingregime. We discuss the thermalisation figures of merit and the differentexperimental procedures to asses thermalization. We compare the definitions oflasing and condensation thresholds. Finally, we explore the fluctuations of thesystem and their relation to the different regimes.

Photon Bose-Einstein condensation and lasing in semiconductor cavities