When I see the term social media, I associate it with one way relationships. It is about connecting businesses to customers, not the other way around. It is about connecting self-promoters (for the lack of a better term) to an audience, not the other way around. As you said: the focus is on the individual, may that be a person or a business.
Perhaps we should be making an effort to distinguish between the two environments, to avoid associating connecting businesses and self-promoters to customers with connecting people to each other.