Rawls is proposing a small set of principles to use to build a model that we can use for moral reasoning. But the key difference is that the model's legitimacy (and usefulness) comes from the fact that the conclusions arrived at from using it seem to conform to our moral intuitions.
By our moral intuitions he means, the sense of right and wrong that he and other elites share. Rawls never claimed universality. He argued that different societies would have different conceptions of justice. The purpose of his model was to act as a heuristic device for reasoning about the "hard" questions. In other words, if the model conforms to 99.9 percent of our moral sense, then when we get to the margins and have trouble deciding, the model becomes our guide.
The important thing to keep in mind is that he and his likeminded sophisticates have already made up their minds about what "decent" people think, and use that to make the model. But most people don't realize that that's what's going on, because on the surface—meaning, before you wrestle with his impenetrable prose—his method seems to resemble the Enlightenment approach of Hobbes and Locke (and, arguably, Rousseau).
Rawls says nothing about right and wrong, or even justice. Instead, he says what the "smartest people in the room" have already decided.