F-Droid has special FOSS Apps only. Aurora Store delivers the same Apps like Play Store.

It’s an alternative client to the Play Store. It does not access F-Droid repos.

Others answered you, but aurora also has an F-Droid replacement called Aurora Droid.

Aurora store is basically anonymous access to the official Google Play store.

You can download any app because unlike the Google Play store Aurora doesn’t send your phones hardware ID, so if for example your phone is rooted you can get the Disney Plus app anyway.

Fdroid is an alternate app store. They have different things than the Google Play store. They respect your privacy and will let you download any app that is ever been uploaded to them, Even old versions of an app.