Learning and generalization in spatial domains is often thought to rely on a "cognitive map", representing relationships between spatial locations. Recent research suggests that this same neural machinery is also recruited for reasoning about more abstract, conceptual forms of knowledge. Yet, to what extent do spatial and conceptual reasoning share common computational principles, and what are the implications for behavior? Using a within-subject design we studied how participants used spatial or conceptual distances to generalize and search for correlated rewards in successive multi-armed bandit tasks. Participant behavior indicated sensitivity to both spatial and conceptual distance, and was best captured using a Bayesian model of generalization that formalized distance-dependent generalization and uncertainty-guided exploration as a Gaussian Process regression with a radial basis function kernel. The same Gaussian Process model best captured human search decisions and judgments in both domains, and could simulate realistic learning curves, where we found equivalent levels of generalization in spatial and conceptual tasks. At the same time, we also find characteristic differences between domains. Relative to the spatial domain, participants showed reduced levels of uncertainty-directed exploration and increased levels of random exploration in the conceptual domain. Participants also displayed a one-directional transfer effect, where experience in the spatial task boosted performance in the conceptual task, but not vice versa. While confidence judgments indicated that participants were sensitive to the uncertainty of their knowledge in both tasks, they did not or could not leverage their estimates of uncertainty to guide exploration in the conceptual task. These results support the notion that value-guided learning and generalization recruit cognitive-map dependent computational mechanisms in spatial and conceptual domains. Yet both behavioral and model-based analyses suggest domain specific differences in how these representations map onto actions.