iOS devices with cameras allow the user to "zoom" into the image being captured. This does not move any lenses or anything; it is a digital zoom and is conceptually equivalent to cropping in post.
However, I would like to know if there is any (however small) difference in output between an image that is captured while zoomed in and one that is only cropped after the fact.
In digital zoom, the camera scales up the pixels to give out the photo with the same resolution as with no digital zoom photo. In cropping, the cropped photo has lower resolution compared to the uncrossed photo.
So I can say that digital zoom is conceptually equal to cropping and then scaling the cropped photo back to its original resolution. The output photos would be the same if the scaling algorithms used in digital zoom and in post scaling are the same.
About the only thing I know is different is that when the photo is cropped after the shot is taken, it will take up more space than if the camera was zoomed in when taking the picture. Why? Because in iOS, photo editing is non-destructive. The part that was cropped out will always be there, you just can't see it. However, when zoomed in, that part of the photo was never taken, so, obviously, it doesn't exist.
Also, currently (iOS 9), one can't edit a Live Photo and retain the Live part of the photo. Though, I believe iOS 10 allows one to edit Live Photos.
Aside from that, there's really nothing. Like you put in your post, it's just digital zoom and basically is retroactively zooming the camera in.
Austin Blanco has done some experiments to answer this question for the iPhone 6s: http://www.austinblanco.com/blog/iphone-6s-zoom-resolution/
It seems that the camera hardware's maximum resolution is not utilised when you are fully zoomed out. This means cropping and scaling a fully zoomed out image will leave you with a poorer image than if you zoomed in some way first before taking the photo.
However, it seems the camera hardware's maximum resolution is being utilised after zooming in just 30% of the way (i.e. ~1.5x zoom). So if you want a final image zoomed in more than 1.5x, there's no great need to zoom in beyond 30% of the way before taking the photo; you can just crop it later if you want (ignoring minor losses due to re-encoding).
