We just returned from the 3/16 7-day Eastern on the Magic and here is what I experienced. There was a "formal night" inwhich people dressed "formal" for their regular dinner rotation meal, which included a Captains Reception immediately afterwards (for us, we were in early dining). The Reception was in the lobby with waiters wandering with appetizers and drinks.
I wore a long black skirt with a beaded top; DH wore a navy suit; DD (age 16) wore a long dress; DS (age 14) wore black pants, white button shirt with tie. We were dressed appropriately. There will be some there dressed more elaborately (including tuxes and evening gowns) and some dressed less formally then we were.
There was another 'formal night' for regular dinner rotation which meant I wore a short black dress, husband in the same suit jacket (different shirt and dress pants); DD in a shorter dress and DS in dark green dress pants and shirt (no tie). Again, we were dressed appropriately.
Then there is Island Night for another one of your dinner rotations and the appropriate dress is wild, colorful dresses and shirts. Disney prefers no shorts at any of their dining rooms.
I was a bit confused on all this, too. But once I figured out that the "dress nights" meant dress for your regular dinner rotation, then it became more clear. Your Personal Navigator will tell you what nights are formal and Island. You can always call Guest Services, they are very helpful.
TIP: If you have shirts or clothes to press for Formal or Island Nights, do so before the day of ... the laundry rooms can get a bit busy the afternoon of these nights with people waiting to use the irons. Hope you enjoy it all as much as we did!