Basically, are the badges that a user can be awarded on StackOverflow the same as the badges that can be awarded on any of the StackExchange sites?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Not always. For example, this badge comes with 4000 rep bonus attached to it :) Area 51 has some specific badges too.
But usually, there's little reason for site-specific badges.
Not that I'm aware of. Of course, there are two kinds of badges: the "regular" badges (for specific "feats"), and the tag-badges. Those are of course (somewhat, there's overlap) site-specific.
In case you don't know what a tag-badge is: you get them for upvotes for answers on questions of that tag. To get the "discussion" bronze tag badge, you need 100 upvotes for answers given to questions tagged "discussion".