There can be visible differences between a leaf shutter and a focal plane shutter when the slit of the focal plane shutter is small compared to the picture and something in the scene is moving fast.
Basically, motion blur at short shutter speeds will look different. Imagine a car zipping thru the frame horizontally, and a focal plane shutter traveling vertically. The car will look a little skewed, since the top and bottom are imaged at different times. With a leaf shutter, everything is exposed at the same time, so the subject will just be blurred in the direction of motion. Note that this blurring will happen with the focal plane shutter too, since the exposure time is the same. Both will be equally blurred, but the focal plane shutter picture will also show the car skewed.
Flashing, like florescent lights and some LED lights, will look different too. With a focal plane shutter you sometimes get bands of light and dark since different parts of the image were exposed when the lamp was bright and when dark. With a leaf shutter, the entire image will be too light or too dark, assuming you set the exposure for the average illumination.