In recent years, discourses around “personalized,” “stratified,” and “precision” medicine have proliferated. These concepts broadly refer to the translational potential carried by new data-intensive biomedical research modes. Each describes expectations about the future of medicine and healthcare that data intensive innovation promises to bring forth. The definitions and uses of the concepts are, however, plural, contested and characterized by diverse ideas about the kinds of futures that are desired and desirable. In this paper, we unpack key disputes around the “personalized,” “stratified,” and “precision” terms, and map the epistemic, political and economic contexts that structure them as well as the different roles attributed to patients and citizens in competing future imaginaries. We show the ethical and value baggage embedded within the promises that are manufactured through terminological choices and argue that the context and future-oriented nature of these choices helps to understanding how data-intensive biomedical innovations are made socially meaningful.