Community based leaderboard level games?

I'm not sure how to call them, but I recently got super into these games, where every time you complete a level, you can see a leaderboard of the people who've done that level best and your world rank in it, whether it be in the shortest amount of time like in Lovely Planet or Dust Force, or using the least amount of resources like in Poly Bridge.
I find these games lovely. And the 3 I mentioned above have amazing soundtracks as well. I definitely recommend checking them out.
If any of you know what to call this genre, or any more of these games, please let me know!
Also if you'd like to share your ranks and scores I'll be happy to see that too! ;3

 

Although Osu! does fit that description, it's definitely different from the 3 I mentioned. Osu! is a rhythm game, in which you're supposed to improve your skill over time, while the ones I'm talking about are more about finding a creative solution to each level. Although they still may require mechanical skill.