Since OM and IE are consistently overlapping fields, I have used the definition prescribed by MIT Sloan School of Management and Institute of Industrial Engineers to define and differentiate both of them.
MIT Sloan School of Management definition of OM: Operations Management deals with the design and management of products, processes, services and supply chains. It considers the acquisition, development, and utilization of resources that firms need to deliver the goods and services their clients want.
Institute of Industrial Engineers definition of IE: Industrial engineering is concerned with the design, improvement and installation of integrated systems of people, materials, information, equipment and energy. It draws upon specialized knowledge and skill in the mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results to be obtained from such systems.