It depends on the context.
Suppose there were 40 students at a summer school, and 10 of them were American; they could be referred to as 'the Americans', so your first sentence would fit that context.
On the other hand, suppose at a US airport there is a distinct procedure for American citizens (I don't know there is, but make that assumption for the sake of the example). Any American who gets off a plane uses one table; the airport authorities refer to it as 'a special table that Americans use'.
I bet Humble will have a fuller explanation than this!