I see several people have replied to this saying that, for all intents and purposes, the Internet is the same as public, and that one should assume everything one does in public will end up on the Internet. "If you didn't want pictures of you doing shots at the bar to show up on Facebook, you shouldn't have been doing them," is the thrust of the argument, I believe.
The problem with that concept of "public" is that real-life "public" is limited by both time and space. Let's say I get blind, stinkin' drunk one night and, in a paroxysm of bad judgement, strip naked and run around my block. I have certainly abandoned the expectation of privacy, because I'm out of my own house and in a public space. But, I can also reasonably assume that, if no one sees me (let's say it's 3:00 AM on a weeknight), the incident will remain unwitnessed. Also, let's assume I'm totally wrong, and everyone on the block is awake, and they're all having huge parties in their front lawns. There is still a limit to the number of people who could see me (based on height, for instance, the density of the crowd, and visual obstacles like trees and cars), and there is a limit to the duration of the, erm, exposure. In other words, once I've done my lap, they're not still seeing me naked.
Let's add a complicating factor. Let's say one person is taking a picture of someone in the front yard and I run through the shot as it's taken. Time is now no longer a factor, because there will be a picture of me running around naked effectively forever. Still, it's one picture, and only so many people can look at it at a time. Even if copies are made, there is a limit to how many people can see it at once.
And finally, the Internet. Let's say the picture winds up on the Internet. Now, not only is there no limit as to the number of people who can see it, but there's no limit to the amount of time it can be seen. This is the least amount of privacy one can possibly have.
The importance in the distinction between "regular public" and "Internet public" is that the Internet provides an unnatural amount of exposure, beyond what one would reasonably expect in the normal conduct of daily life. One might reasonably anticipate walking down the street and being watched by other people on the street, or even winding up accidentally in someone's photograph. It's a far different thing to be photographed or videoed and have the results on the Internet for posterity. Sort of like being under constant surveillance by everyone with a Internet access. That's beyond public.