There is a difference. It's a bit long to explain.
A party at my house.
I have some drinks already fixed or some bottles opened, and I know the people who came will at some point want to have a drink.
I would then ask:
- Who wants a drink?
Now, suppose, I have some assembly that is not a drinking party, but, say, a meeting, an informal one, where it is permissible for a person to sip something while participating. But it is possible people won't ask for it, as it is, after all, not a drinking party, but a working meeting.
I would ask:
- Does anybody want a drink?
Now, during the same meeting, if there is no alcohol permitted, and drinks may be only non-alcoholic ones, like Coke or water, I would ask:
- Does anyone want something to drink?
I actually agree with the Walrus: Who wants a drink? - I know that there are people among you who want a drink. Who are they? Does anybody want a drink? - Just shooting in the dark - I do not know if anyone wants a drink, but I hope someone does...