The present article aims to distinguish between a sociocognitive and a sociocultural approach to forms of “collective” creativity. While the first is well-illustrated by studies of group or team creativity, the second has generally supported investigations of collaborative creativity, most of them performed in the last few decades. The comparison between these two fields takes different levels into account, from the epistemological position adopted to issues concerning the theories and methods used. Special attention is given to reviewing models of creativity. However, although the literature on group creativity contains several cognitive models, there is a scarcity of such constructions for collaborative creativity. This is why a secondary aim of this material is to introduce a sociocultural theoretical framework and discuss its implications for developing situated models of creativity. In the end, the similarities and differences between the two paradigms are examined with reference to both theory and research and arguments are given for why it would be beneficial for sociocognitivists and socioculturalists to engage in a more consistent dialogue.