Where are you getting your definition for social media?
Wikipedia defines social media as [1]:
Social media are interactive computer-mediated technologies
that facilitate the creation and sharing of information,
ideas, career interests and other forms of expression via
virtual communities and networks.
I don't know if there's an "official" agreed upon definition somewhere, but I do know this: The definition of what social media is and what it will become is not yet known -- it will continue to evolve as the Internet evolves and as our understanding evolves closer to true -- but at its core, I would say social media is technology that enables bidirectional public communication among people whereas mass media [2] enables unidirectional public communication -- one to many broadcasts to people -- with no direct feedback loop.
The Internet provided the foundational infrastructure and was the prerequisite layer that made social media interaction possible. What we do with social media -- how we use it, build upon it, and optimize for it -- is yet to be determined.
For example, who would have envisioned the mobile phone as we use it today when the telephone was invented. Phones aren't just used for phone calls anymore. The iPhone changed that, but the iPhone couldn't exist in its present form until the foundation for the Internet infrastructure was laid. Today our vision of the Internet is not what it was when it was invented. It continues to evolve, as does its uses and definition. Social media will be like that too -- it's part of the next layer to build upon, and we're still learning what that is -- its definition is still being formed, and its optimal form is still to come.
[1] https://en.wikipedia.org/wiki/Social_media
[2] https://en.wikipedia.org/wiki/Mass_media