I know this topic has been discussed before on Stack Overflow. But there are still some things that are not clear when I read previous posts about it. So here they are:
You can think of the difference between shared preferences and an SQLite database in terms of data size but that isn't entirely accurate. A better way to think of it is in terms of the structure of the data you want to store.
Shared preferences can only store key-value pairings whilst an SQLite database is much more flexible. So shared preferences are particularly useful for storing user preferences, e.g. should the app display notifications etc. Whilst an SQLite database is useful for just about anything.
Both data sources are local but something you should be aware of is the ability to backup your application data to cloud storage that is linked to the user's Google account. This makes it much easier for your users to change devices and for their applications to easily transfer to the new device. For more info take a look here.