Scholars across disciplines increasingly hear calls for more open and collaborative approaches to scientific research. The concept of Open Innovation in Science (OIS) provides a framework that integrates dispersed research efforts aiming to understand the antecedents, contingencies, and consequences of applying open and collaborative research practices. While the OIS framework has already been taken up by science of science scholars, its conceptual underpinnings require further specification. In this essay, we critically examine the OIS concept and bring to light two key aspects: 1) how OIS builds upon Open Innovation (OI) research by adopting its attention to boundary-crossing knowledge flows and by adapting other concepts developed and researched in OI to the science context, as exemplified by two OIS cases in the area of research funding; 2) how OIS conceptualises knowledge flows across boundaries. While OI typically focuses on well-defined organisational boundaries, we argue that blurry and even invisible boundaries between communities of practice may more strongly constrain flows of knowledge related to openness and collaboration in science. Given the uptake of this concept, this essay brings needed clarity to the meaning of OIS, which has no particular normative orientation towards a close coupling between science and industry. We end by outlining the essay's contributions to OI and the science of science, as well as to science practitioners.