It’s representative democracy; precisely how representative is too representative (that is, how many layers of insulation there is from the actual decision to the will of the people) is something that gets debated over and over, often in the context of the Electoral College, which is (or seems) especially far removed from the common voice compared to, say, how Senators are currently chosen. (Compare how Senate elections work now to how they worked in 1800.)
So. My contention is that ‘democracy’ is currently used to mean “The people choose their government to the largest extent in free and fair elections and referenda.” That’s certainly what, for example, the ‘Democracy’ in ‘Spreading Democracy’ or ‘Making the World Safe for Democracy’ means; approximately nobody is currently out there fighting for direct democracy, where everything is put to a popular vote.