  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.
