Bella's Lullaby and A River Flows in You by ma. Who said they were the same? ?

I wanted to learn how to play "Bella's Lullaby" on the piano. So when I looked up the sheet music, everything directed me to "A River Flows in You" by ma. There are even youtube video of people playing the piano titled "Bella's Lullaby" but it's the same as "A River Flows in You." Now, when I got the soundtrack, it sounds nothing like it. I was wondering who championed that. Who said that "Bella's Lullaby" was "A River Flows in You?" And where can I find the ACTUAL sheet music to "Bella's Lullaby" by Carter Burwell as featured on the soundtrack?