"Digital media" is not intrinsically interactive.
Digital media can be as uni-directional as any old line media form - podcasting, for instance, may be a participatory creative expression, but is consumed passively. In spite of the "on-demand" quality of much digital media, it's often simply another outlet, no more or less interactive than any other channel.
"Interaction", beyond its typical digital skew, however, is defined as "two or more objects having an effect on each other". Yep, two or more. So also leaving aside the definition of "object", we can (wildly) extrapolate that "interactivity" is intrinsically social. So does "interactive" media = "social" media? Maybe. But I sucked at college calculus.
One definition of "Social Media" (the term is like "a tale told by an idiot, full of sound and fury, signifying nothing. or anything. which is pretty much the same. but don't believe me, believe Dare Obasanjo) can also be defined as user-perpetuated marketing, like "Word of Mouth" (WOM). Viral marketing (one of my most hated terms) is just digitally fueled WOM. And marketers and agencies are working hard to figure out how to leverage social media (in all its forms, from viral videos to social networks, to blogs and beyond) to create, enhance, and grow brands. One because it makes sense. Two, because it is perceived to be cheap.
Why pay for advertising, when people talking about your brand is the most effective advertising out there (WOM=#1 influencer of purchase intent)?
Because they need to know what to talk about.
One scenario sees a campaign tip with a paid effort that morphs into a social media effort, but they are hard to plan - the "I put it out there, you talk about it" is great in theory, but if it doesn't work, well...it doesn't work. I could slip my message into YouTube or put empty cans behind clubs to create buzz. it doesn't much matter. Engage me or lose me, sailor. We like that interactive is not just a digital thing. And social media isn't either. They happen to be good enablers, but they have to be used right.