A significant difference between the two is that there is no set standards for religious proofs. For one person, the Sun suddenly breaking through the clouds and shining down after a storm might be considered a sign from Heaven. Another religious person might require a more portentious sign, such as a vision of an angel. In that sense religion is a very personal pursuit. Science, although certainly not immune to interpretation of its theories and results, strives to remove the personal factor as far as possible.
Science requires rigorous physical proofs.
Of the theories advanced for the creation of the Universe, the Big Bang has the greatest amount of physical evidence supporting it. It does not in any way disprove religious beliefs. For some, it is reasonable to believe that if the Universe had a Creator, that Creator also ordained the physical laws by which it was formed and evolves. The Steady State theory is no longer considered seriously because it cannot explain aspects of the evidence, such as the Cosmic Background Radiation, without making some rather large assumptions. It really fell flat because attempts to reconcile it with the observations of the Universe were too contrived.