We report on a real-time observation of the crossover between photon and exciton-polariton lasing in a semiconductor microcavity. Both lasing phases are observed at different times after a high-power excitation pulse. Energy-, time- and angle-resolved measurements allow for the transient characterization of carrier distribution and effective temperature. We find signatures of Bose-Einstein condensation, namely macroscoping occupation of the ground state and narrowing of the linewidth in both lasing regimes. The Bernard-Douraffourgh condition for inversion was tested and the polariton laser as well as the photon laser under continuous wave excitation were found to operate at estimated densities below the theoretically predicted inversion threshold.