When asked to indicate which items from a set of candidates belong to a particular natural language category inter-individual differences occur: Individuals disagree which items should be considered category members. The premise of this paper is that these inter-individual differences in semantic categorization reflect both ambiguity and vagueness. Categorization differences are said to be due to ambiguity when individuals employ different criteria for categorization. For instance, individuals may disagree whether hiking or darts is the better example of sports because they emphasize respectively whether an activity is strenuous and whether rules apply. Categorization differences are said to be due to vagueness when individuals employ different cut-offs for separating members from non-members. For instance, the decision to include hiking in the sports category or not, may hinge on how strenuous different individuals require sports to be. This claim is supported by the application of a mixture model to categorization data for eight natural language categories. The mixture model can identify latent groups of categorizers who regard different items likely category members (i.e., ambiguity) with categorizers within each of the groups differing in their propensity to provide membership responses (i.e., vagueness). The identified subgroups are shown to emphasize different sets of category attributes when making their categorization decisions.