The term ‘social business’ has several meanings. Nobel laureate Mohammed Yunus and others within the non-profit and charitable sector use it in this sense:
A social business is a non-loss, non-dividend company designed to address a social objective. The profits are used to expand the company’s reach and improve the product/service.
It seems that this term is more widely used internationally than in the US, where it appears less frequently. In the US this expression is less familiar, I think.
Meanwhile, ‘social business’ has come to mean something else altogether in the web community. It has been derived by analogy with terms like social tools, social media, social networks, and so on. These form a network of related terms in which ‘social business’ is a natural and obvious extension, that I define in this way:
An organization designed consciously around sociality and social tools, as a response to a changed world and the emergence of the social web.
I guess we are destined for convergence in these terms. And someone has to go edit the Wikipedia page, too.
[thanks to Thomas A for reminding me to clarify this.]