A key question in creativity research concerns whether creativity is best understood as domain-specific or domain-general (Baer & Kaufman, 2005). Yet, the literature is plagued with insufficiently defined notions of domain specificity and generality of creativity. For example, researchers have alternatively discussed domain-generality as either a positive manifold (i.e., positive interdomain correlations), or as a unidimensional factor model (e.g., Ivcevic, 2007), without acknowledging the difference or providing a justification for their particular choice. We argue that there are diverse ways to conceptualize domain generality and specificity, with different implications (Kan et al., 2019). We propose to unscramble confusions in the literature by defining taxonomy of models that imply a general factor, domain specific factors, both, or neither. We review statistical frameworks used to test and compare them, examine their implications, and invite creativity researchers to clarify how they conceptualize and formalize generality and specificity in their research. Statement of educational relevanceA clear representation of how creativity is structured across domains is fundamental to the understanding of how creativity is to be learned and trained. Notably, the existence of a general creativity implies that creativity might be learned and trained in general (i.e., across multiple domains), while domain specificity implies that it might be learned primarily at the domain (or subdomain) level. Beyond the traditional framing of this question as a dichotomy or continuum of generality-specificity, we argue that there are in fact many types of conceptual and statistical models for understanding the structure of creativity across domains, which have different implications.