Yes and no. The first 3 nights are "regular rotation" menus. The restaurant served the same menu for 3 nights, but you're in a different restaurant each night. So, if you eat in Triton's/Lumiere's your first night, you'll have a new menu on night 2 in, say, Animator's Palate. And the people who are in Triton's on the 2nd night will have the menu you had night 1.
After the first 3 nights, once everyone's been in each restuarant once, the menus are the same for all restuarants, but change each night - Pirate Menu is served in all 3, then Captain's Gala is served another night in all 3.