OPs is closer to the truth; the shift from network -> media shows a useful distinction between what the focal point of activity is.

Note that "social" (as in social interaction with people you know) in "social networking" is a requirement, while it is not in "social media". You may as well call it "parasocial media" since that is the way most people use it most of the time.

Thus 'social media' is primarily based on content, while 'social networking' is primarily based on social connection and interaction.