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Most of the characters don't go by their Disney names, presumably to avoid litigation from the famously brand-protective corporation: Jasmine is only known as "The Princess," Abu is only known as "Monkey," and Iago isn't even named. The titular vizier, who went by "Jafar" in the original Aladdin (1992), is here called "Ja'far." The one exception is Aladdin, whose name existed centuries before Disney adapted the story.
When Sherrezade first meets Jafar, she says "They cut off my ear because they didn't like my face." Jafar says "That's barbaric!" and Sherrezade responds with "Hey, it's home." This is an original line from the opening song in Aladdin "Arabian Nights". The line was altered for the VHS/DVD release and soundtrack reissues as it was deemed too offensive.
The character Sherrezade and the song 1001 Nights is from the book Arabian Nights. Scheherazade spends a night with the king who plans to execute her in the morning. Each night, she tells him a story and refuses to tell him the ending until the next night. On the 1001st night, she runs out of tales, but by this time the king has fallen in love with her. He spares her life and makes her his queen. The story "Aladdin's Wonderful Lamp" is from this collection of tales.
In addition to poking fun at Disney movies and the history of the Disney and Pixar studios, the story also parodies the musical Wicked: The Untold Story of the Witches of Oz. In fact, when Ja'far is first seen, he is reading Wicked and summarizes the plot to the bookshop owner.