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App Indexing actually uses deeplink kind method but helps you to achieve different goal. In a simple business scenario you would want if user searches for your business from mobile browser he should get app link and that link open different screens for different urls (search keywords). As you can see post so far talks about keywords, searches that means App Indexing is more about search engine optimization keeping mobile apps in mind and App Search Optimization too.
About deeplinks they are simple urls (or url set) that we define in our app and tell mobile system that if matching url is clicked our App can also handle it.
In case of deeplink there can be several apps claiming to open same url but app indexing result will open only your app.
I hope this answer clarifies things well.
In simple words:
App Indexing is to make app searchable from google.
Deep Linking is to open the app activities by an url.