On iOS a URL scheme needs to be setup usually. (e.g. itms:// links open the iTunes store app). I don't think there's a right way to do this really. Half the time I'm frustrated a link didn't open in the app and the other half I'm frustrated it didn't just open in the browser.
You're correct, iOS apps can only handle schemes but now whole URLs. On Android, the system can intercept any URL and pass it to the app (http://instagram.com/blahblahblah goes to the Instagram app, for example), which means web URLs can open in apps instead. On iOS, you must use a dedicated scheme, which means links from the web don't play nice with apps.
Opener attempts to fix this by mapping web links to app-specific links.