We show that while orbital magnetic field and disorder, acting individually weaken superconductivity, acting together they produce an intriguing evolution of a two-dimensional type-II s-wave superconductor. For weak disorder, the critical field H_c at which the superfluid density collapses is coincident with the field at which the superconducting energy gap gets suppressed. However, with increasing disorder these two fields diverge from each other creating a pseudogap region. The nature of vortices also transform from Abrikosov vortices with a metallic core for weak disorder to Josephson vortices with gapped and insulating cores for higher disorder. Our results naturally explain two outstanding puzzles: (1) the gigantic magnetoresistance peak observed as a function of magnetic field in thin disordered superconducting films; and (2) the disappearance of the celebrated zero-bias Caroli-de Gennes-Matricon peak in disordered superconductors.
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