Like most people, we say Teacups. Spaceship Earth is the Epcot Ball, Rio de Tiempo is the Boat Ride in Mexico, TTA is the People Mover.
I don't think shortcut names count (like Peter Pan for Peter Pan's Flight).
Is it still officially called MGM, or is the correct name Disney Studios?
I usually forget whose castle is whose (between WDW and DL) so I just say The Castle. (BTW, which is which? I'm too lazy to look it up right now - lol).
Hotels - I'll probably never remember that the Disney Inn is now Shades of Green, or that the whole complex is Port Orleans and there is no more Dixie Landings. My kids call the Contemporary "the monorail hotel", even though the monorail stops at GF and Poly also. (And I know people who call it the Toaster, too).
But I am happy to say that my whole family not only gets the names of the parks right, but even now knows many of the abbreviations I use in our schedules (MK, MGM, EpFW, EpWS, AK).