Thats probably screen-tearing then. It occurs when your card is feeding more FPS to your monitor than it can display (typically 60FPS), so the monitor can sometimes glitch and display half of one frame and half of the next one. Thats why the image appears to be disjointed at the tears. Vsync limits the FPS to 60FPS so you dont run into issues such as screen tearing.
Recording the game wont show screen tearing as its a fault of the monitor, not with the card.
This video may help, though it deals more with the Adaptive V-Sync on some Nvidia cards.http://www.youtube.com/watch?v=DAiPmazmR_M
Anyway, getting a 120hz monitor will allow you to display up to 120FPS before you will run into issues like screen tearing.
Screen tearing can happen at any FPS, when v-sync is not on. Even if you have 2 FPS on a 60hz monitor, you can have screen tears. 120hz does not solve that.
However, a 120hz monitor, due to updating the screen image twice as often, will not have as much latency when v-sync is on. When a GPU misses the window to send an image to the monitor, it has half as long to wait until it can be sent in the next window.
The reason that tearing happens regardless of FPS, is simply a matter of the GPU not caring when the monitor is updating its image unless v-sync is on. This allows the GPU to update an image at the same time the monitor is displaying it. I do have a 120hz monitor, and I get screen tearing at 60 FPS, 30 FPS, 90 FPS and 120 FPS if v-sync is not on. However, I get far less latency with v-sync on with this monitor than my previous 60hz monitor.