Characterizing creativity in visualization design can lead to the design of more expressive representations and visualization authoring tools that prioritize human creativity. In this paper, we examine how creativity manifests itself in visualization design processes through two complementary studies. First, a systematic review of 63 papers yields a design space spanning three themes: creative design frameworks that focus on developing design processes by incorporating divergent and convergent thinking activities, creative visual representations that focus on developing unorthodox visualizations, and visualization-enabled creativity support tools that focus on supporting a creative task (e.g., writing) with visualization. Second, we conducted qualitative interviews with 11 visualization practitioners and researchers to understand practical challenges and contrast those with current academic framing through our design space. The interview findings indicate that artifacts or final products (unorthodox visualizations) are often disproportionately considered as the primary indicator of creativity, whereas the design process remains undervalued in practical and organizational contexts. We also found that ideation is a universal bottleneck, and organizational constraints are often the primary barrier to creative work. We discuss implications for rethinking the relationship between our design space categories, addressing organizational barriers, and designing future frameworks, tools, and evaluation methods that better support creativity in the age of AI-assisted visualization. The full list of coded papers is available here: https://vizcreativity.notion.site/coded-papers.