Both of these philosophers—and it is worth noting that Rousseau had read Aristotle—grappled with the concept of self-love, believing one form of self-love to be healthy and virtuous. Aristotle wrote in book 10 of the Nicomachean Ethics that one kind of self-love was worthy of reproach: that practiced by people who "assign to themselves the greater share of wealth, honours, and bodily pleasures." The problem with this kind of self-love was that it infringed on the ability of others to live good lives. People practicing this only sought to gratify the basest of human instincts. True self-love was that of people who always tried to act virtuously. These people would actually wind up, Aristotle argued, receiving the acclaim and wealth that others seek.
Rousseau, writing in the eighteenth century, also described two types of self-love, which he called amour-propre and amour de soi. Amour-propre as Rousseau described it was the desire to receive approval and respect from others. He thought that this form of self-love was corrupt and inauthentic, stemming from the development of society among mankind. He viewed this as a departure from mankind's original state. In his Second Discourse on Inequality, he articulated another type of self-love, one which he attributed to man in the state of nature. He called this amour de soi, and it refers to the human drive to satisfy our most basic needs, like food and shelter. This was completely inwardly directed, unlike amour-propre, though it existed alongside another concept that Rousseau called pitie, which he took to mean something like "sympathy." Amour de soi was healthy and natural; amour-propre artificial and corrupt.
Thus, while both philosophers believed that there were two types of self-love, they conceived of these concepts in almost completely different terms. Aristotle thought virtuous self-love took into account man's place in society, while Rousseau argued that inward-facing self-love was the healthiest of human instincts.