Ice box to me means container which you can add ice to, to keep things cold... ie beer.
Usually if designed properly it'll also have a drain (if it's a fixed ice box)...
Everything else that actively cools would be either an air conditioner (room sized) or a refrigerator (box sized). If it does a particularly good job of actively cooling, we'd call that a freezer.
Pretty sure that's universal code in RVs too.
I suppose ice box is a better term than waterproof cabinet with drain.
To ME this is an ice box (where you had to go to the store and buy blocks of ice)... or if you were really special dry ice... but whatever.