Of course, realism isn't something that is fixed, or objective. It has been debated over the ages. But that philosophical debate we can leave aside for the moment. Instead let's look at a few particular examples of screen "realism".
Take Neorealism. It has been celebrated as the very essence of screen realism but if you look at a film like The Bicycle Thieves (1948), it's a fairly conventional story, sentimental, with many scenes obviously shot in a studio, and with fake rain in certain scenes. On top of that, the whole concept is fake. Had this been in real life this man's life wouldn't have been dependent on one bicycle, and one bicycle alone. He would've got a new bike, and even if he hadn't, surely, among his many clever friends, a bicycle would've been found, built, purchased. It's a good film, and it says a lot about Italy in the years after the war and after Mussolini. But it's still a manipulative film which alters reality when reality gets in its way.
Today realism is often equated with grainy, blurry photography, shot with a camera in perpetual motion. But when we look at the world, it's fairly stable and clear. Nothing grainy about it. In fact, it looks the very opposite of how "realistic" film looks. I suppose one reason for that choice of filmmaking is that it's supposed to look like home movies, what it would look like if you'd made it yourself in your home. Only, even then, we try to hold the camera as steady as possible, we don't shake it on purpose.
I'm not implying that this way of filming is something new, John Cassavetes for one did it in the 1960s, but the last 10 years it's become fairly mainstream. And it's got nothing to do with realism; it's only a style among many styles, and one that more often than not draws attention to itself as such. Among the many strange demands made by the Danish Dogme 95 movement, the one about the camera being handheld was one of the strangest.
In Die Hard: With a Vengeance (1995), the director John McTiernan excels with a handheld camera. That doesn't make it a particularly realistic film. No, realism in cinema, as in all art forms, has very little to do with style, and more to do with feelings, characters and situations. And, as André Bazin wrote "realism in art can only be achieved in one way - through artifice".
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For notions of realism, have a look here.
The Bicycle Thieves have been released under different titles. In the US it was called The Bicycle Thief.
This post was amended and a few errors corrected 2014-05-01.
This post was amended and a few errors corrected 2014-05-01.