Let's begin with a quick overview of what each of the different models would entail.
Utilitarians, following Jeremy Bentham and John Stuart Mill, both nineteenth-century British philosophers, hold that the greatest good consists of providing the greatest happiness to the greatest number of people. Utilitarianism is part of the broader theory of consequences which holds that an action is good insofar as it maximizes good consequences. In the case of utilitarianism, the consequences are utility, which is measured in terms of individual happiness. For them, social justice would require policies that make the greatest number of people as happy or well-off as possible.
Karl Marx, the nineteenth-century German philosopher, claimed that social justice consists of egalitarianism—everyone having a roughly equal amount of relevant resources. In such a society, there would be no income inequality.
Social contract theories date back to the Roman philosopher Lucretius, but the more recent versions are associated with Thomas Hobbes, John Locke, and Jean-Jacques Rousseau (from the seventeenth and eighteenth centuries). A recent version was defended by Timothy Scanlon. Theorists are not committed to a particular substantive version of social justice: they argue that what's just is determined by a contract, implicit or explicit, between the citizens who make up a given polity.
The United States today is a combination of the utilitarian and social contract theories. Policies and laws are made with an eye toward the greatest good—this reminds one of utilitarianism. They are justified, however, on the basis of a social contract.