I've never realized that Disney's The Little Mermaid was not an original Disney character/story, though this shouldn't have been a surprise since Disney's princesses all come from stories developed by people outside of Disney. Like Disney they take someone's original story and add so much more to them to make them appropriate and more appealing to children of all ages.
Andersen and Disney both share the similar story lines when it comes to the main idea of the story. In both The Little Mermaid stories, Ariel wanted to ultimately become human so that she could be with Eric. She also sided with Ursula in a deal that would give her legs in exchange for her voice; in Disney's version her voice was kept in a nautilus shell by Ursula, in Andersen's version she actually gave up her tongue. She wouldn't stay human forever if she didn't end up with Eric. The punishments were different in both stories if she didn't end up with Eric, and both punishments did happen in one way or another. Andersen's story says that if Ariel didn't marry her on the dawn of the next day after he marries another woman she will die brokenhearted and will disintegrate into sea foam; however in Disney's version Ariel will return to her regular foam but will belong to Ursula.
Ariel gets her legs and is fine physically according to Disney, but in Andersen's story every time she moves it feels as if she is being stabbed in the legs and her feet bleed terribly. Eric also falls for her until Ursula deceives him by using Ariel's voice leading him to believe that she is the one that saved him, therefore he wants to marry her. It's a big commotion at the wedding and Ariel eventually gets her voice back and when Eric tries to kiss her to make the transition complete, the sun sets and Ariel is returned to mermaid form and kidnapped by Ursula.
In the other story the prince thinks the woman he saw at the temple where he was put after being rescued was the one that saved him, so...