Check your camera settings.
Your left view seems to be orthographic and the right view with perspective. If you want to render orthographic you have to set up your camera as orthographic too.
Looks to me like it is just a matter of perspective. It appears to me like the eye location in the right viewport is close enough to the object for perspective distortion to become significant. The left one is either further away or in orthographic mode (I cannot check just from the image).
In the camera settings change the view on the camera can get some really strange and interesting results.
These are under the camera icon.