Open innovation holds great potential for improving the efficiency of companies' innovation processes, but also presents substantial risks. A key issue in innovation management is finding the right balance of openness, i.e., determining how open companies should be in their innovation activities. However, academics and business practitioners hold conflicting notions of what constitutes open innovation practice and of how "open innovation companies" are defined. In this paper, we present three in-depth case studies of global R&D-intensive companies, where we find that the firms' perception of their openness differs from their actual situation (as determined by the innovation practices that they apply), and that each company has a different view as to what constitutes open innovation. We claim that resolving conceptual ambiguity and differentiating between openness (as a philosophical aspect) and open innovation (as a way of structuring the innovation process) in research is critical in order to clarify the current state of open innovation research and enable the communication of results to practitioners.