In common parlance in the United States (outside the academic or scientific communities), researchers and scholars both engage in investigation. A scholar investigates and studies documents. When one thinks of a researcher, one thinks of imperical research, which does not usually involve studying documents (e.g., a researcher may investigate the number of migratory birds in a given location). This is the difference. The fact is, however, these terms overlap significantly, and if you ask an actual researcher or scholar what the difference is, the answer may be more detailed than you care to receive.