These songs are performed by Utada Hikaru, they are the songs from both main series of Kingdom Hearts.
Kingdom Hearts: Intro is the remix of Simple and Clean, end scene is the proper studio recorded version.
Kingdom Hearts 2: Intro song is called Passion.
Which song do you like better?
Me, I prefer Passion, I love both songs though, and most of her music, I have her Albums imported, and for those who didn't know she is also a representative icon for Kirby, promoting new Kirby games for Nintendo.
I really hope there's an awesome song to top Passion for Kingdom Hearts 3.