No, Watch emails you a bunch. Stars just show up in a list so you can find it later. That being said, public bookmarks always seemed weird to me. Why not just actually bookmark it with your browser? Not that it matters.
App provide better UI and UX for mobile devices. It's faster, easier to navigate (bottom navigation) and some features work in it which don't on the mobile site (I can't remember which views force desktop view).
I know, that's what I'm saying. We were talking about stars and then you said I should look into Watches instead, but what I was saying is that I don't like watches because you get emails. Customizing which emails doesn't help with that. Apologies if I was confused about something.