How do I separate two devices currently sharing one backup?

I've had an old iPod Touch for years, but recently upgraded to an iPhone 5s. When I first plugged the iPhone into my mac, iTunes asked if I wanted to restore from an existing backup or create a new one. I chose to restore from the iPod, thinking that would give me a good starting place with all my existing apps, and I'd modify from there.

I didn't realize, though, that in doing that I made my computer see them both as essentially the same device. When I download a new app on my iPhone (which, usually, is not compatible with the old iPod that can't run an iOS past version 6), it automatically downloads the same app to my iPod. Or, maybe it's just an update of an app I still want on the iPod, but probably the updated version won't run on the iPod (or I'd have already updated it.) I'd like to give the old one away to my fiancée, who doesn't have a smart phone or iPod of any kind, but it's a problem that the two devices want to sync all their data.

I could just wipe the old iPod, but it would be very difficult for my fiancée then to find apps that work with it, seeing as it's still on iOS 6. Very little that you can find in the app store today is compatible with it, and the app store seems to be incapable of filtering to show just the ones that are. It also doesn't make it easy (or possible?) to download older compatible versions of apps that have since updated. Much easier is to leave on the apps that are already there, and which work with the iOS and iPod as is.

So, now that I've already told the computer to update the iPhone from the iPod's backup, and I've gotten what I wanted out of that backup, how do I separate them again? How do I tell my computer to back up what's on my iPhone separately from what's on my iPod, as distinct devices instead of syncing them both as one?

Thank you!