Over the last few decades, two domains have undergone seemingly similar transformations: Closed innovation turned into open innovation, closed science into open science. In this essay we engage critically with recent calls for a close coupling of the two domains based on their apparent commonality: openness. Comparing the historically-specific ways in which openness has been defined and mobilised, we find substantial differences between open innovation and open science. While openness in innovation was developed as an analytic concept and redefined quite flexibly over time, openness in science was created as a programmatic concept and its initial definition has been preserved rather rigidly. Contrasting openness in innovation and science helps anticipate some of the unintended consequences that a close coupling of these domains might yield. A close coupling might alienate advocates for change within the academic community, marginalise maintenanceoriented collaborations between science and practice, and increase the dependence of science on profit-oriented platforms. Reflecting upon these unintended consequences can help policy-makers and researchers to fine-tune their concepts for new forms of engagement across the science-practice divide.