Honestly, all you have to do is listen to both the 2nd and 3rd season themes to know they're different. The very first note of the 3rd season theme is a higher pitch and doesn't even sound like the same instrument. Then a harp thingy comes in a second later that's not in the 2nd season recording. The vocal is mixed differently also. The 2nd season sounds like a singer, the 3rd is more ghostly.
IIRC, union rules required the theme be rerecorded every year.