How is bangle different from other smart-watches?

All those watches however have in common that they have a main screen for the watchface, then you can navigate apps/widgets. Is Bangle the same?

More or less. You have a main watchface and that usually also displays widgets at the top/bottom (battery level, steps, bluetooth status, etc) which you can choose. Then you can install many different apps as well (including more watchfaces) - they all live on the watch and can be executed without needing a host phone.

Is it able to trigger events, notifications and so on?

Yes, with Android you get event notifications using Gadgetbridge and can accept/reject calls/etc or control music. There's currently no specific way to push custom data back to the watch with Gadgetbridge though - you'd have to write your own app (Web Bluetooth or otherwise)

It's worth checking out https://banglejs.com/apps/ to see what's available at the moment in the way of apps if you're interested.

Let us know if you have any other questions!