At low laser intensity, the coupling between photons and electrons in a direct gap semiconductor gives rise to a coupled mode known as the exciton polariton; in this mode, the exciton appears as a non interacting boson. Under intense laser irradiation made of below-gap photons, this coupling gives rise to a blue shift of the exciton line which increases with the laser intensity. This effect known as the exciton optical Stark effect, is due to interactions between (virtual) excitons. At small detuning, Coulomb interaction and Pauli exclusion contribute to the shift, while at large detuning the shift is controlled by Pauli exclusion only. It is then identical to the shift of a two-level atom for a semiconductor having one valence and one conduction band, while it is the shift of a (2+4) level atom when the conduction band is twofold and the valence band fourfold. The cross-over between the exciton-polariton and the exciton optical Stark effect takes place when interactions between excitons cannot be neglected, i.e. when there is more than one photon (or virtual exciton) per exciton Bohr radius. These two effects correspond in fact to the same phenomenon: an exciton dressed by photons, the photon density being either small or large.