Look up UIDocumentInteractionController. It's been around a while.

You can also do quite a lot with URL Schemes but more apps need to implement support and publish their requirements.

There is also the X-URL-Callback spec which could be implemented by more apps. Google is using this spec on iOS.

http://x-callback-url.com/specifications/

https://developers.google.com/chrome/mobile/docs/ios-links

https://developer.apple.com/library/ios/documentation/uikit/...

Finally, let's get away for guessing about what Apple might be doing. It was easy enough to search "iOS open in" to find this support to support this feature and it had been around a few years. There's no reason to suggest that Apple is copying Android on this feature.