I asked once before and was advised i needed to purchase a registration key in order to print a list of my movies.  my question now is, do i need to purchase a key for BOTH the iphone/ipad version and the desktop.  Or do i need only purchase one, regardless of why I would do it. (in other words what does purchases both for pc and ios device get me).  can i print a list if I ONLY buy the registration key for my IOS device

The desktop version offers much more functionality than the iOS version. While the iOS version does work as a stand-alone program, I consider it to be a great addition to the desktop version and not a replacement. Buying only the iOS version won't be enough in your case, buying only the desktop version will be.

That said, the iOS version has some advantages to the desktop version. It's just so much more comfortable to simply scan your new purchases with the camera in your iOS device than manually entering the UPC. And for entering personal information like the watched and loaned status, it is much easier to simply grab your phone instead of going to your computer.

So for what you want to do, it would be enough to just buy the desktop version. Get the iOS version if you want some added comfort. Also keep in mind that it is a one-time purchase fee. You won't be charged again for updates.