I suspect most folks "interchange" BBQ and grill as one in the same device, you get heat and food cooks on it.
You can make a "grill" slow cook for things like pulled pork by turning flame down and not placing food directly over the burner (IE Indirect heat). You can even turn a gas grill into a "smoker" just by adding a smoking box which uses wood chips or a smoking tube which uses smoking pellets.
You can even use a griddle top on a grill or BBQ..
It is a pretty universal device..
Extend a stays were interesting devices and if OP could find one they still will not be able to use the built in propane port and would have to use the BBQ at the trailer tongue..
Personally, they could simply buy a refillable 5 lb cylinder and call it a day also.