The shocking truth is that the US is just one of many, many, many democracies. There’s nothing uniquely American about democracy.
The American system was based on the French implementation, which in turn was based on the British implementation.
What is unique about American democracy is the scale. The biggest issue that America has is that the current incarnation is not fit for purpose - it’s a system that when used like it is, creates massive vote inequality, gives some “elected officials” what amounts to jobs for life and spreads blame so thin that (heaven forbid!) should someone try to create a dictatorship, it would be very hard to stop it.
If you want the characters to be confused, but not the players, pop in some classic tropes.
Two that spring to mind:
Transporter technology - High pitched noise, swirly patterns, a vague sense of being dissolved, then the reverse.
Impossibly sterile rooms - no obvious furniture, panels on the walls automatically open to provide things, beds rise out of the floor, etc.