From what I have experienced Social Media, is more about communicating out your message through digital channels. (Frequently used in Marketing.)
While Social Business is more about People, Process and Technology and how digital collaboration integrates into your daily work life. How you could use social tools within and outside the company to stay engaged, transparent and nimble as a business.
Particularly how employees can work together in company systems, collaborating and adding value.
Resulting in a network of engaged employees, that are collaborating, contributing value and creating a Social Business.
In summary, a Social Business is engaged through its employees, transparent in its communication and able to quickly adapt to business challenges.