To understand human learning and progress, it is crucial to understand curiosity. But how consistent is curiosity's conception and assessment across scientific research disciplines? We present the results of a large collaborative project assessing the correspondence between curiosity measures in personality psychology and cognitive science. A total of 820 participants completed 15 personality trait measures and 9 cognitive tasks that tested multiple aspects of information demand. We show that shared variance across the cognitive tasks was captured by a dimension reflecting directed (uncertainty-driven) versus random (stochasticity-driven) exploration and individual differences along this axis were significantly and consistently predicted by personality traits. However, the personality metrics that best predicted information demand were not the central curiosity traits of openness to experience, deprivation sensitivity, and joyous exploration, but instead included more peripheral curiosity traits (need for cognition, thrill seeking, and stress tolerance) and measures not traditionally associated with curiosity (extraversion and behavioral inhibition). The results suggest that the umbrella term "curiosity" reflects a constellation of cognitive and emotional processes, only some of which are shared between personality measures and cognitive tasks. The results reflect the distinct methods that are used in these fields, indicating a need for caution in comparing results across fields and for future interdisciplinary collaborations to strengthen our emerging understanding of curiosity.