This study explored differences in children's information seeking in the two exploration tasks aligned with proposed curiosity frameworks. One task provided an open-ended unlimited information seeking design assessing the frequency of exploration attempts across similar options; the second was a constrained information seeking design with limits on how much could be explored, focusing instead on what children chose among varying levels of uncertainty. Children's information seeking did not relate between the two tasks, and children give different explanations for their motivation for seeking information that aligned with the different designs; in the open-ended task children's exploration was motivated by more superficial and perceptual features, while in the constrained task they described desiring information and mentioned uncertainty and mystery. Potential implications of the results are discussed. [This paper was published in: "Proceedings of the 47th Annual Meeting of the Cognitive Science Society," edited by D. Barner et al., 2025, pp. 5743-49.]