The clearest distinction is that modern scientists work within the material world. They use the scientific method to generate hypotheses and test them through observation. Science does not deal with what cannot be tested and either verified or rejected, i.e. religion and people's beliefs concerning the spiritual world. Science, by definition, operates from a secular worldview.
The traditional shaman, on the other hand, seeks to harness, or at least mediate with the powers of the spirit world for benefits in the material world, most notably in the area of healing and medicine. Like scientists, shamans also generate predictions, but these come in the form of prophecy, not testable hypotheses. Of course, a shaman whose prophecies never come true or who always fails to heal his or her patients might completely lose their spiritual authority, and certainly shamans can reach conclusions about certain natural medicines through trial and error. Ultimately, however, there exists no rationalized, systematic method for verifying the claims of shamans.