The Little Mermaid is really based off of the real story written by Hans Christian Andersen. In this story, Ariel does save the prince and falls in love with him. She visits the sea witch and trades her tongue for legs. Every step Ariel takes feels like walking on sharp shards of glass. The deal is somewhat similar, however if the prince doesn't marry her, she will die. Ariel eventually fails to marry the prince. Instead of dying, if she kills the prince, she will return to being a mermaid. Although, Ariel's heart just can't handle it, and she throws herself off the balcony, turning into sea foam as she hits the shore. She finds herself in some sort of purgatory, where she will have to pay off good deeds until she gets an eternal soul. This could take about 300 years.
Ariel saves Prince Eric from drowning and falls in love with him.
Ariel visits Ursula the sea witch and trades her tongue for a pair of legs.
Prince Eric finds Ariel and is determined to bring her home and marry her.
Ursula tricks Eric into marrying her instead of Ariel.
With the help of animal friends, Ariel marries Prince Eric in a happily ever after.