Both. A republic with representative democracy which involves the selection of government officials by the people being represented. The most common mechanisms involve election of the candidate with a majority or a plurality of the votes.
A republic is a state or country that is not led by a hereditary monarch, where the people of that state or country (or at least a part of that people) have impact on its government, and that is usually indicated as a republic.
I know some like to confuse the issue but the truth is both.
The United States is a Constitutional Republic, which in Western terms is pretty much the same as a Representative Democracy. The founding fathers certainly wanted to get away from the evils of Monocracy they saw from England and much of Europe of the time.
In a pure Democracy, every citizen would be called to vote on every issue (technically, anyway), and they were worried about that, too. Not even from the logistics, but based on the idea that the average person may not be wise enough to protect the lesser among us.
Thus the Representative Democracy… the citizens elect representatives, in theory learned people who will not simply represent their best interests, but represent the best interests of the collective, which includes the needs of the weak and the minorities.
To an extent, many of our Founding Fathers were both economically and intellectually elite… they really didn’t trust the average person to always make the right decisions. Thus, the founding of ":a Republic… if you can keep it":, as Ben Franklin was quoted.
By the strictest of political theory definitions, the United States is a Constitutional Republic. The ":republic": component means that the government itself is chosen from members of the populous. This, as opposed to a monarchy, for instance, but ALSO could also be a theocracy, (governed by a religious person or ideology) a xenocracy, (rule by an external body or country) or many other options. The Constitutional component refers to a series of laws that govern how the government is allowed to act. This means that once the officials are in office, they have to abide by more than just the desires of those they represent.
A democracy, however, is quite literally, ":a government by the people,": meaning that the people govern themselves and each other. All political debates and decisions are made by the populous itself. Outside of some small tribes in South America, there are no true democracies currently in existence.
Its A Constitutional Limited Republic
Technically we are a constitutional republic: A constitutional republic is a state where the head of state and other officials are elected as representatives of the people, and must govern according to existing constitutional law that limits the government’s power over citizens.
The United States is a Democracy with a Republican form of Government.
Where most people get confused is saying America has a Democratic form of government.
A democracy, means the citizens freely elect their government.
In a democratic form of government, the citizens directly elect their government.
In a republican form of government, the citizens elect electors, who then elect the government.
That’s sort of like asking whether Donald Trump is a millionaire or an entrepreneur. We are BOTH democratic and a republic. We are a democratic republic.
I believe that it would technically be called a Democratic Republic. It uses aspects of both.
We lost the Republic as our founders envisioned– when the 17th Amendment was put in effect.