I bought an iPhone 6 and did a restore from an iTunes backup, and now all the apps that came standard with the iPhone 6 are missing (they don't show up under "purchased" either)

I lost my trusty 4S and had to buy a new phone. I went with the iPhone 6 and they had me set it up as new in the store. When I got home, I did a restore from my last iTunes backup, but now all the original apps that came standard on the iPhone are missing. They aren't listed under "purchased" either in iTunes or in the App store on the phone itself. I'm not sure what is actually missing since I only got a glance at it, but I think it's things like iTunes U, Garage Band, Pages, etc.

I'm also missing one 3rd party app (Calvetica) that doesn't show up anywhere. And finally, the actual "Photos" app is missing as well and all I have is the Camera Roll.