"I am the shadow on the Moon at night, filling your dreams to the brim with fright."
Oogie Boogie Shadow is, as the name implies, the shadow of Oogie Boogie.
The Nightmare Before Christmas
Oogie's Shadow appears on the moon in the song "This is Halloween". It was also supposed to be in the "Oogie Boogie's Song" dancing with physical Oogie, but the sequence was taken out of the finished product due to time restraints. The scene itself is what the director Henry Slick didn't agree on because it's only 17 seconds long!
The Nightmare Before Christmas: Oogie's Revenge
The first boss in the game is a shadow-like Oogie Boogie, whom Oogie calls his "mere shadow." After a fight between Jack and the shadow, Boogie escapes. Later, what appears to be the real Oogie Boogie fights with Jack, in his casino, before the foe reveals himself to be Oogie's shadow in disguise. Jack, in this level, destroys the shadow.