We examine how core professional and institutional actors in the innovation system conceptualize climate change adaptation in regards to pluvial flooding-and how this influences innovation. We do this through a qualitative case study in Copenhagen with interconnected research rounds, including 32 semi-structured interviews, to strengthen the interpretation and analysis of qualitative data. We find that the term "climate change adaptation" currently has no clearly agreed definition in Copenhagen; instead, different actors use different conceptualizations of climate change adaptation according to the characteristics of their specific innovation and implementation projects. However, there is convergence among actors towards a new cognitive paradigm, whereby economic goals and multifunctionality are linked with cost-benefit analyses for adapting to extreme rain events on a surface water catchment scale. Differences in definitions can lead to both successful innovation and to conflict, and thus they affect the city's capacity for change. Our empirical work suggests that climate change adaptation can be characterized according to three attributes: event magnitudes (everyday, design, and extreme), spatial scales (small/local, medium/urban, and large/national-international), and (a wide range of) goals, thereby resulting in different technology choices.