Hey there. I've been reading for a while and not posting, but here in the CDZ, I'll give it a shot. For background, I'm a historian and former history and poli sci teacher, with an MA in American History from a well-regarded military university. I'm an Independent and live in a swing state. None of what I'm about to say is a secret; you all should have learned it in high school at the latest.
A lot of people here are using the terms 'democracy' and 'pure democracy' interchangeably, but they're not the same thing. 'Democracy' does not literally mean that we're all citizens; it literally means 'government by the people.' It means that the power to make change in a society rests with the people, as opposed to an autocracy (power lies in one person) or a theocracy (power lies in the church) or many others.
One type of democracy is a 'pure democracy' (also called a direct or an Athenian democracy). In this model, every member of the electorate gets together to vote on every motion. Obviously, even in our earliest days that would have been beyond impractical, so we have never been a direct democracy.
Another type of democracy is a 'representative democracy,' where we each elect a representative from our area to go to the capital city and cast votes to represent our area's wishes on each motion. That's what we have always had, where (on the federal level) we each elect one Representative and two Senators, plus a varying number of Electors, to represent our wishes in Washington. We have a representative democracy, which is a democracy, so yes, we are definitely a democracy.
Separate but related to all of that, we are also a republic. 'Republic' comes from the words for literally a "public thing," meaning our government is owned by us, the people, rather than being owned by a monarch. In a monarchy, executive actions are done in the monarch's name, laws are passed in their name, and judgments are made in their name, but we don't do that. In our republic, the Chief Executive derives his authority from the office of the President as elected by the people, and their powers are limited only to the Executive. The legislators and Justices similarly derive their authority from their offices and their powers are limited to their branch. That's what it means that we are a republic; lots of people have limited power to do just their one job, rather than all of the power being derived from one ruler. We are also a republic.
In the modern context, it is difficult to imagine a government that is a republic without also being a representative democracy, and vice versa, so in practice the terms are basically interchangeable. The upshot is this: The American system is, and has always been, both a republic and a representative democracy.
A final note: The insistence that we are 'not a democracy' is almost always traceable back to someone who wants to weaken our democracy. It's not always malicious, but there is always someone out there saying it who is. They are very good at making it sound convincing, but don't fall for it. Your high school US Government teacher already solved this mystery, years ago.
