It depends on the resort. At WCC, the bottomless milkshake can be ordered as a beverage. At LeCellier, the smoothies can be ordered as a beverage. These are "for sure--we got em" as of May. At some other places, the milkshake or smoothie can be ordered as a dessert.
In general, the beverage is bottled water, lemonade, tea, fountain drinks, etc., but there are some exceptions. The server will tell you at these restaurants. Lemonade, iced tea, and fountain drinks are unlimited refills at TS. Milk is generally not refillable at dinner...again, I'm sure there are exceptions.