Quoting Wikipedia:

“The Fifty Shades trilogy was developed from a Twilight fan fiction series originally titled Master of the Universe and published by [E. L.] James episodically on fan fiction websites under the pen name ‘Snowqueen Icedragon’.”

Exactly so. It was not able to be published in its initial state as a Twilight fanfic due to copyright and had to be re-worked so as not to infringe.