Do dogs see television and other "screens" the same way we do? For example, if they see a dog on TV, would it look to them like a dog on TV without any "distortion"? The reason I think there may be distortion to them is because TV is designed for our eyes (e.g. red, green, and blue "dots" that match the receptors in our eyes). This is somewhat related to this question: Do dogs really only see in black and white?.
There are several factors that affect your dog's perception of a TV or other screen.
Perception of motion: Display devices rely on displaying a rapid sequence of still images to produce the illusion of motion (the phi phenomenon). Dogs have a higher flicker fusion threshold than humans, so a screen that appears to show continuous motion to humans might appear to "flicker" to a dog.
Color: Dogs have two color receptors in their retinas, whereas humans have three. This means that they can distinguish fewer "hues" or types of color than humans. They can still tell whether light is coming from the low (red/green) or high (blue) frequency ends of the spectrum. So what a dog sees may be somewhat similar to a human with red-green colorblindness.
Other senses: Scent is a major factor in how dogs perceive the world, so a dog may not react to TV images the same as they would to real-world objects. Similarly, dogs have more acute hearing than humans which can affect their reaction to real versus recorded sounds.
Psychological factors: Even if a dog can "see" what is on the screen, it might not be able to actually recognize and identify objects.
Unfortunately I don't have any scientific evidence to back it up or generalize further, but while our pug does recognize animals on a screen, it does not seem to be in the same way a human would.
She reacts to most images of animal-like movement, with or without sound (as evidenced by a television on mute). This can be as small as a dog or fox moving in the distance or a bear lumbering through the middle of the frame. She reacts to both live action shots as well as cartoon or computer animated images. Movement seems to be easier to spot, as she reacts much more strongly to a moving animal than a still image.
Our pug recognizes sounds as well as images, and she will bark as a response to the noises of another dog or animal on the screen.
In fact, if there is something particularly interesting happening on the screen, our pug will run around and look behind the screen to try to find it. As a puppy, she would also howl and complain to us that this interesting thing was missing, as if we needed to fix it.
With that said, the primary sense of a dog is smell, not sight. The image or video on the screen may look and sound realistic, but unless it has the appropriate smell, your dog will be able to easily tell that it is not a real animal.