Responsibility as Moral Obligation
This definition assumes that responsibility is a matter of honor or duty. According to this definition, “When someone recognizes a duty, that person theoretically commits themself to its fulfillment without considering their own self-interest.”

Moral responsibility typically assumes that individuals are in possession of free will and have a high degree of agency. Someone subscribing to the idea of moral responsibility might conclude that the moral thing to do is to pay off all individually acquired debts (1) in full, and (2) as quickly as possible - even if doing so has a negative impact on one's quality of life.

Thus, even though someone might be legally entitled to income based repayment, such a choice would be considered unethical because society ends up shouldering some of the individual borrower's burden.

Social Responsibility
Social responsibility assumes that there is a tradeoff between economic and social benefit, and tries to find balance/equilibrium between the two. For example, higher levels of education are associated with longer life. Additionally, more educated people are typically healthier and less likely to participate in criminal activity, especially violent crime.

A society might consider shouldering some of the costs of individuals' higher education to be an acceptable tradeoff. A long, healthy life in a safe environment is a tremendous benefit to citizens. The health problems and crime associated with a less educated citizenry might cost more than education would. In that case, society might even be able to recoup some or all of the cost of providing that education.

Are the tradeoffs reached by any particular society on a given issue necessarily optimal? I am not sure that can ever be known for sure. Society is complicated, and it's impossible for any individual to see the entire picture.

For example, lots of people think the American way of debt is not healthy. However, if it's a social construct, is society responsible for changing it? Does social responsibility lead to a diffusion of responsibility where we all complain but no one works to change things?

Food for Thought
Responsibility is a powerful concept. How do you determine when and where to draw the line?

Human beings are a diverse lot, so there are many definitions of responsibility out there. What do you do when someone else's idea of responsibility is different than yours? Is one school of thought on responsibility more or less valid than another? If so, who gets to make that determination?