Question about music and instruments...

This is a pretty esoteric thing to ask here, I think, but I don't know where else to ask.

I recently downloaded a piano app to my phone despite having no musical skill. I messed around a while and eventually figured out how to play songs from The Legend of Zelda: Ocarina of Time. If you didn't know, music in Ocarina of Time is played on an ocarina (natch), using the A and four C buttons (up, left, down, and right). Anyway, I figured out how to play the song that goes C-Up, C-Left, C-Right, C-Up, C-Left, C-Right (Epona's Song) on the piano. Cool. Next, I figured out how to play the song that goes C-Down, C-Right, C-Left, C-Down, C-Right, C-Left (Saria's Song).

At this point I became very confused because the keys on the piano app that corresponded to C-Left and C-Right in Ocarina were different depending on which song I was playing. When playing Saria's Song, C-Left would be the A note and C-Right would be the B note, but when playing Epona's Song C-Left was B and C-Right was C. I have no idea how this is possible.

I dug Ocarina of Time out of mothballs and confirmed that the buttons always play the same notes every time, and I compared the piano app to a real piano to make sure the notes it played were accurate, and I found no answers. How is it possible that a note that's always the same is simultaneously different in the context of different songs? Is it sorcery?

I remember there were pitch variations using other buttons, but beyond that, whatever is telling you those notes must be playing in a different key than the original, or something.

Epona's Song

Saria's Song