We consider the competition between spin singlet pairing and itinerant ferromagnetism whose magnetization is yielded by a relative shift of the bands with opposite spin polarization or by asymmetric spin-dependent bandwidths. Within the framework of the exact solution of an extended version of the reduced BCS model, the structure of the coexisting state is shown to have general features that are not related to the character of the ferromagnetism. The role of different types of ferromagnet is then investigated for the proximity effect in a system made of a bilayer junction with a spin singlet superconductor interfaced with a ferromagnet in the clean limit. We show that the qualitative behaviour of the proximity effect does not depend on the nature of the ferromagnetism. Differences emerge at the borderline with the half-metallic regime. For the spin-dependent bandwidth type of ferromagnetism the pairing amplitude exhibits an oscillating behaviour until the density of the minority spin carrier becomes almost zero. The crossover from an oscillating to an exponentially damped profile occurs away from the half-metallic limit when a spin exchange type ferromagnet is considered.