If you buy a fountain soft drink in a park, it will be handed over in a Coca-Coca branded paper cup. If you then want to dump that cup into your refillable container, that will be fine, but if you want more, you are going to get yet another Coke-branded paper cup with each drink that you purchase.
The only restaurant in the parks that I can recall offhand that has a self-serve fountain that allows unlimited refills is Epcot's Electric Umbrella. There are CM's standing attending it, and you have to have that branded cup to use the fountain; they will warn you off it you attempt to fill a container other than the cup sold in the restaurant.
I have no idea about what rules might apply on a cruise.