Can't speak for many, but I do both things. Not facebook specifically, since I try not to do too much of it at work (with varying success), but reddit and HN and such. Taking little breaks and reading a blog post or something can be fairly relaxing, and sometimes if you're stuck you can switch gears and come back to the problem with fresh eyes.

There's also 'background processing', which happens during physical activity (had a coworker who left around 2 to go running and rock climbing, getting her most productive time in after going home at around 4 or 5pm), chatting with coworkers, getting a snack or some water, that kind of thing.

They're separate, but I (and most folks I know) do at least a little of both.