John Rawls's account of the common good is arguably just an amalgamation of individual goods. His famous metaphor of the veil of ignorance makes this clear. The common good is the distribution of resources, positions, and opportunities in a given society that a reasonable person would choose if they didn't know who they were going to be in that society. The common good, then, is about protecting every individual persons' interest and is not separate from the good of individuals.
Martha Nussbaum's account is, it could be argued, more sophisticated. Nussbaum's work has to do with distinctively human capabilities. In this regard, she is more Aristotelian in her thinking about the human person than Rawls is, and therefore is also more committed to an Aristotelian vision of the common good. On this account, the common good is more than just an amalgamation of the goods of individuals.
Because human beings are characterized by a distinctive set of capacities (reason, for example, is part of what makes a human creature human), they are also characterized by a particular sets of goods and ends. Different social orders can make the achievement of those ends more or less possible. A core argument of Nussbaum's is that it is possible for a social order to be arranged in such a way that it precludes the achievement of human goods and ends entirely, at least for a large portion of the population (this is what actually existing societies have done to women).
The common good, then, isn't just making sure that everyone has resources on the basis of the principle of justice as fairness. The common good is that set of conditions necessary for every individual member of a society to actualize their fundamental human capabilities.