I think it's the same melody, for that main verse. It's just another example of popular music ripping off the Classics which previously ripped off popular music. Twinkle Twinkle wasn't written by Mozart, but he did compose a series of melodies based on what was a popular folk melody.
There are innumerable (literally) examples in music where hits are revealed as thinly disguised versions of something or other by Puccini or Bizet, etc, etc. Lloyd Webber has made a career out of it.