Software engineering, especially design and requirements engineering, is intensely creative. However, practitioners and researchers appear to perceive creativity differently, hindering knowledge transfer. To explore and understand these perceptual differences, this paper combines a systematic mapping study of SE research literature with an interview study of practitioners. The subsequent analysis of 84 primary studies and 17 semi-structured interviews reveal some agreement (e.g. creativity is a process that produces novel and useful ideas). However, it also reveals important differences in the way creativity is conceptualized, measured and improved. These differences undermine evidence-based techniques to enhance and measure creativity in SE research and practice.