For prayer, the appointed period acts as a container for performing the act; different prayers may be conceived within a time frame, making the identity of the prayer important. For a Ramadan fast, the day serves as the measure of the worship and generates different rules.
It would be mistaken to argue that because both acts take place within time, every rule of intention must be identical. Similar outward circumstances do not themselves prove a shared operative cause.
Sickness, travel, makeup fasts, and vows can modify the details of fasting intention; those cases should not be indiscriminately merged into the ordinary resident’s Ramadan fast.