Hmm... This is a pretty interesting question!
1. Magic Kingdom
It's not a drastic difference, but my folks and I would call the Swiss Family Treehouse the "Swiss Family Robinson" instead. We simplify The Magic Carpets of Aladdin to just "Aladdin," and we call Walt Disney's Enchanted Tiki Room the "Tiki Birds." The same thing applied while it was Under New Management.
We refer to the Walt Disney Railroad as just simply "the train," Country Bear Jamboree to "Country Bears," and Liberty Square Riverboat as "the boat."
My parents goof often with names, and would call Mickey's PhilharMagic "Mickey's Philharmonic." We also greatly shorten Prince Charming Regal Carrousel to just "the carrousel."
Tomorrowland Speedway to "race cars," Astro Orbiter to "rockets," and we have always referred to the Tomorrowland Transit Authority as "The PeopleMover." You can thank my mother for engraining that name into my head ever since I began visiting.
My parents would also sometimes call Stitch's Great Escape! as just "Lilo & Stitch."
2. Epcot
Spaceship Earth as "The Globe," Universe of Energy as "Ellen, The Circle of Life as "Timon & Pumbaa," Journey Into Imagination as "Figment," and my parents might refer to Captain EO as just "Michael Jackson." I'll likely wind up calling Agent P's World Showcase Adventure as just "Perry the Platypus."
3. Hollywood Studios
Indiana Jones Epic Stunt Spectacular! as "Indy," Star Tours as "Star Wars," Voyage of The Little Mermaid as "Ariel," Disney Junior: Live on Stage! as "Playhouse Disney," and The Magic of Disney Animation as "You wanna draw some characters?"
4. Animal Kingdom
We don't go to the park much, but: It's Tough to Be a Bug! as "A Bug's Life," Festival of The Lion King as, "The Lion King," and sometimes Expedition Everest as, "Mt. Everest."