Yes, the app is completely different once you are on
DCL wifi. It can then be accessed by everyone, even those without a Disney account. (It will ask for name, stateroom number, and birthdate.)
The app used onboard (and in the terminal) will show exactly what is happening on your cruise, including locations, times, and descriptions of all activities for kids, families, and adults; operating hours for all food and beverage areas; dining room menus; charges to your stateroom account; option to purchase a placeholder for your next cruise; and ability to mark and view selected activities.