Sub 4 and Sub Mini are the Sonos subwoofers on sale, and both run on the Sonos app.
Sub 4 pairs with an amplified non-portable Sonos product such as Arc Ultra or Era 300. Sub Mini needs at least one amplified non-portable product such as Era 100 or Ray.
Sub (Gen 1) and Sub (Gen 2) work with the S1 Controller as well as the Sonos app. Sub (Gen 3) works with the Sonos app only.
The Sonos app is the current app. The S1 Controller is a separate app for older products. The generation of a product (Gen 1, 2 or 3) shows in the System section of the Sonos account page.