The difference is that a social contract is a concept and not literal contract.
The actual reality behind "the social contract" is simply that people have the capability to act in ways that can and do affect other people. Because of this, most people find that it's beneficial to moderate our actions in relation to other people based on their preferences.
I'm referring to very real obligations that we are all held to under the justification of "the social contract" such as taxation and being drafted into military service, not social niceties.
We are held to these obligations as seriously and as legally as we are held to real contracts, but unlike the bedrock that constitutes the basis for the legitimacy of all real contracts, these obligations are imposed upon us with no opportunity for consideration, consent, or rejection.