When you purchase a movie or TV show from the Apple iTunes store you can transfer it from your computer to a mobile Apple device. But up until recently the rules for iTunes rentals were a bit more complicated. The terms stated that you couldn’t transfer movies or TV shows rented using an iPhone 4, iPod touch, or Apple TV… but only stated you couldn’t transfer movies rented on an iPad.
The new version of the rule doesn’t make any distinction, and states that any content rented on any device is only viewable on one device at a time. You can transfer rentals from a computer to a mobile device, but that’s it. If you rent a video on your iPad and want to watch it on your Apple TV before it expires, you’re out of luck.