The things you see in new games nowadays. Some arbitrary awards for doing something "special" (fighting off some melee specialist mob in hand-to-hand combat 100 times, killing over 4 people with single grenade, having over 90% accuracy in single game with at least 10 kills, 5 perfect scores in row, etc.). Usually these are meaningless badges, but some games actually give in-game bonuses for these or some other "benefits" such as unlocking characters, weapons or other features.
These are awarded to the player, not some character or characters in the game, so there's the difference. Although some may be only awarded when done with a specific character.
Some newer platforms have these as a "must" feature, so I'm not sure if they should be marked with it or not.
This should not include things that are automatically gained at specific points in the game, regardless of how you played it.
Edit: Team Fortress 2 seems to be famous for these, although they impart no benefits as far as I can tell.
This could be generalized as unlockable content, but I think quite a few console games games have that. Or alternatively split to unlockable characters, game modes, in-game bonuses, art, background info, and possibly others. But that may go into too much detail. Characters, game modes and in-game bonuses are the most important.
The difference between unlockable content and achievements is that unlockable content is usually granted when you find some secret object or similar but can sometimes be done through some achievement like deed as well.
When I started tagging games with it, I was initially interested in the kind of rewards that have impact on gameplay (in-game bonuses, unlocked items/characters, etc.) instead of simple fan cruft (e.g. concept art). And the instances where these were granted only if the player accomplished something exceptional (something not required to play the game through, but may be something difficult to pull off or some otherwise impressive or obscure feat).