Differences between Android and iOS Intents and Sharing

I have read several articles saying one of the key advantages of Android is sharing between apps and that iOS doesn't allow sharing between apps. I don't understand Android enough to understand the differences. This is to foster that discussion.

My impressions are: Android apps can register for intents and intents can be used for both file sharing but also inter-app operability. Android apps can also choose to expose portions of their data for cross app search.

iOS apps can register to handle file types and another app can choose to share a file with your app. My impression is that the built-in apps don't use this (ex: no specifying a handler for save movie files in the mail app)?