It's both. The first one is where the story first appeared, and the second one is the two princess volumes collected together in one book, so it's the same story in there.
I looked at it myself, and Ursula skinny is still purple but she has black hair, and her hair is actually parted just like Vanessa's. It's pretty pathetic.
It's highly doubtful that Disney would base The Little Mermaid III on that story because usually they don't do that. After Cinderella II came out, they made a book where Prudence helps plan Cinderella's wedding. Eventually the Fairy Godmother used magic to make the cake and dress and invitations for her. But this is not what happened in [/]Cinderella III[/i]. A lot of times these books conflict with the movies. There was a book where Ariel imagined what it would be like to marry Prince Eric, and in the beginning she had his statue in her grotto during the whole book, when in the movie she only had the statue for a few minutes before it was destroyed by her father!
Sometimes these books even vonflict with other books. I once read a book where Ursula was already Queen, and she was an evil ruler, but King Triton fought her and he became king. Then there was something about an evil chest... Anyway, that really conflicts with the story amazon980 told us. Also, Ursula was once considered being made Triton's sister. We don't know if she still is or not, but for The Little Mermaid Broadway musical, she was described as his sister in the casting call:
If Ursula is Triton's sister, her being in love with him would be incestuous. It's true, amazon980, that Ursula was in love with Triton in another book. In My Side Of The Story: The Little Mermaid, she was in love with him. But that's the problem with these books. They aren't necessarily canon. They go off saying things that may conflict with the movie or not be true altogether when sequels or later information is revealed.Ursula: To play female in her 30’s or 40’s. A Sea Witch and Triton’s estranged (and none-to-happy-about-it) sister, banished forever for dabbling in The Black Arts.
An alternate link to the one Disney's Divinity provided is: Skinny Ursula
She got skinny with magic during a song she sang. I don't know why she changed her skin color, but that goes along with Disney Divinity's theory that Ursula used magic to become purple because it was her favorite color. Although, there was an episode where she was with Octopans or something, a race of octopus people with blue skin, I believe.