Getting right the broad frame within which we understand the Internet, of course, matters. Just not as much as some people think.
The question of framing the Internet usually arises in a political context. That's where framing gained currency, particularly with George Lakoff's writings. For example: Can we reframe the inheritance tax as a death tax? Can we reframe tax increases as revenue enhancement? Can we reframe a war as a police action? Framing has political effects. And that's why framing the Internet correctly does matter. At the very concrete level, deciding whether the Internet is a communication network or an information network has direct consequences on the jurisdiction of the Federal Communications Commission. Beyond that, at the level in which framing affects how citizens think about matters, Tim Wu's reframing particular network management policies as "Net neutrality" was (in my opinion) a brilliant act of framing that has had some political effects.
So, I don't mean to say that the framing of the Internet doesn't matter. But the Internet is important enough that it will escape our attempts to understand it within a frame that we pick for political reasons.
It's not that the Internet is too unusual to fit into any existing categories. Just about nothing fits perfectly within a category. From health to television, if the concept hasn't been legislated and worked through the courts, it is going to sprawl across many lines. For example, is terrorism a type of warfare or a type of criminality? Does it apply only to stateless groups, or can nations be terrorists as well? (It's easy to forget that until the past 10 or 20 years, the latter was the case.) Can threats of violence constitute terrorism, or does it require acts? We can argue forever about these questions because concepts just don't have neat edges.
Of course, the same is true of the concept of the Internet. Is it a series of tubes? Is it a series of bits? Is it a protocol independent of how it is instantiated? Does it have to be public? Does it include all the content that is now on the Internet? Is it a world apart from the real world, an adjunct to it, or a communication medium within it? Not to mention questions like: Is the Net our new library? Is it a swamp of misinformation? Is it a social place for connecting with friends? Is it for bullies and cowards, pirates and plagiarists?
We can spend forever trying to decide the right framing for the Internet, because it depends so heavily on the political purpose of the framing. So long as there is some truth in the framing, there is no harm in that; much of politics is a contest of frames.
But, ultimately, the framing of the Internet will not be done by us on purpose. It will happen the way all-important re-framings happen, through the imponderable play of history. Take a much narrower example: How did Shakespeare get framed as the greatest English-language playwright and poet? Historians can help us follow some of the path (Contested Will, by James Shapiro, is a very enjoyable book that talks about this a bit), but ultimately Shakespeare got appropriated that way through the chaos of culture. Or, how did white Americans come to view the western frontier as land we inevitably would come to inhabit? We know the phrase came from an 1845 magazine article, but we reframed the continent that way because of an inextricable mix of religion, philosophy, politics, arrogance, fear ...
Grander re-framings are even less explicable and predictable. We can't know yet what the Internet's frame will be. We can only know that it will not come about by everyone thinking it over and coming to agreement. It will just happen.
Until it does, I think it serves a political purpose to continue to push for one particular frame. It's hardly precise and it is certainly not clever. The Internet's best frame is, I believe, exceptionalism. Those of us who love the Net more than seems reasonable need to keep hammering on the fact that the Net is so special that the old frames are not appropriate. The Net is not yet assimilated to understanding, still to be invented, open to possibility, liberating of human and social potential, a framework for hope. If we don't frame the Net that way—if we let it be framed as just another communications medium-that is what it will become.
But the Internet is more than that. I personally believe that it is one of those rare phenomena that does not get framed so much as frames everything else. We are already starting to understand everything as a network with the Internet's characteristics: decentralized, messy, rich in connections, complex beyond comprehension, scaled. From business organizations to decision processes to cellular biology, everything is starting to look like a network, just as 50 years ago, everything started to look like data in a mainframe.
The Internet is framing us.