I mean... when working with such a limited sound chip, I'm sure a LOT of things sound similar if you adjust the speed and pitch.
No. Music doesn't work that way. It has nothing to do with the limitations of the sound chip. It has to do with something called "themeing".
Banjo-Kazooie has it too. There are several variants of any particular level theme to fit the different situations. For example Treasure Trove Cove has a variant for being on land, being near Capt. Blubbers ship, being inside the seashell, being underwater and being in the sand castle.
Every variant has the exact same melody, but the instruments, speed and sometimes pitch are changed to fit the mood of the particular place you are in.
Super Mario Bros. using the same 24 (I think) note melody for collecting a power-up and ending a level are a more primitve form of this. But it has nothing to do with limitations. It's a choice.