Long story short: the US is both a republic and a democracy, but it's complicated!
The United States is known as a "representative democracy," in which citizens directly elect representatives to legislate on their behalf. The United States is also a republic, a system of government in which the power lies with the people, there is a representative government, and there is an elected executive (like a president) and not a monarch/dictator.
There are many similarities between democracy and republicanism, but essentially, a republic is a form of government and a democracy is more of an ideology that inspires how we run our government. It is not a contradiction to say that the United States is a democratic republic, and asking people to choose between whether the United States is a democracy or a republic is a false dichotomy.