Past research has demonstrated that both consequentialist motives (such as deterrence) and deontological motives (such as "just deserts") underlie children's and adults' punitive behavior. But what motives do we ascribe to others who pursue punishment? The present work explores this question by assessing which punitive motives children (6- and 7-year-olds, n = 100; 67% White; 55% female) and adults (n = 100; 76% White; 35% female) attribute to individuals who witnessed and punished a transgression (third-party punishment). Beyond this, we varied the social role of the punisher (a teacher, an adult visiting a school, a fellow peer) to examine whether motivational ascriptions vary depending on social context. Across these contexts, children endorsed a variety of punishment motives but consistently rejected the notion that individuals punish for the purpose of inflicting suffering. Adults--like children--prioritized consequentialist motives but, in more personal contexts (involving a child punishing their peer), considered "just deserts" a more plausible motive. These findings speak to developmental and contextual variation in individuals' theories about punitive motives and provide insight into how individuals understand and respond to punishment in everyday life.