I used to say online vs real world in the past, but switched to deliberaty saying online / offline. Guess that people saying "real world" often hold it against the notion of "virtual world" for our internet cyberspace in their mind's eye, then just say "online".
There is an issue with online vs. offline though, I think. Many people view them just as 'channels'. We have this extra channel to communicate, so now we can be social there, in addiiton to offline. Case closed.
But this is overlooking and underestimating the impact of online communication vs. what we know and do in the "real world". Social norms, habits and culture we are very used to, isn't adopted 1-to-1 online. It isn't all-the-same-but-digital, in significant ways. A world of behavioral differences making online vs offline like different worlds almost, where the rules change.
In IM chat for instance it is relatively common to not answer when queried.