It would be both. In some cases, a researcher or a professor may have an affiliation at more than one institution. Again, it is up to the researcher to identify on that application who their parent institution is, if you will.
It provides flexibility. What we have seen and what we hear in health research is that, because universities serve a wide variety of research interests, health topics may not be necessarily prioritized by the university; however, they would be by the research hospital.