One important function of categories is to permit rich inductive inferences. Prior work shows that children use category labels to guide their inductive inferences. However, there are competing theories to explain this phenomenon, differing in the roles attributed to conceptual information vs. perceptual similarity. Seven experiments with 4- to 5-year-old children and adults (N=344) test these theories by teaching categories for which category membership and perceptual similarity are in conflict, and varying the conceptual basis of the novel categories. Results indicate that for non-natural kind categories that have little conceptual coherence, children make inferences based on perceptual similarity, whereas adults make inferences based on category membership. In contrast, for basic- and ontological-level categories that have a principled conceptual basis, children and adults alike make use of category membership more than perceptual similarity as the basis of their inferences. These findings provide evidence in favor of the role of conceptual information in preschoolers' inferences, and further demonstrate that labeled categories are not all equivalent; they differ in their inductive potential. (Contains 2 figures and 4 tables.)