Recent research indicates that 6- to 9-month-olds understand a number of object words, but the nature of this understanding is unclear. This work examined whether infants restrict these terms to individual objects (like proper names) or extend them across multiple objects from a category (like common nouns). Experiment 1 reports evidence that 6-month-olds comprehend the name for their mother (e.g., “Mommy”) as restricted to the individual person. Experiment 2 offers support for the claim that 6- and 9-month-olds understand both a label that is restricted to an individual person (e.g., “Mommy”) and a label that extends to multiple members of an object category (i.e., “hand” or “ball”). Experiment 3 provides evidence that 12- to 15-month-olds comprehend both a word that is restricted to an individual (e.g., “Fido”) and a word that extends to multiple category members (e.g., “dog”) for the same object (i.e., a pet dog). The findings indicate that infants understand both individual- and categorical-scope words early in development, suggesting that neither lexical type represents a privileged starting point in word learning. We propose that cross-situational learning abilities, along with intuitive biases to conceptualize objects from particular semantic classes as either individuals or members of categories, play a role in infants' learning of words of the two lexical types.