> Short answer: yes. We are a democratic republic but most people think of us as a direct democracy.

Can someone point me out as why Americans differentiate republic from direct democracy? I reckon than in most of the world these words don't mean opposites. Republic means just "not a monarchy/aristocracy" where I live, and I reckon in most of the world.

(This is a genuine question, maybe there is a reason for the American usage of the term)

Generally it's called a republic if there is representative government, i.e. if you have a senate or a congress. Presumably by direct democracy people mean voting directly on issues, in which case I'm not sure there's any state of a significant size implementing that particular form of government.

> Generally it's called a republic if there is representative government

No, if there's an elected representative government, it's generally a representative democracy. Even when (as in the case of the UK) it's also a Constitutional monarchy, and so not a republic of any kind.

> We are a democratic republic but most people think of us as a direct democracy.

A direct democracy is one where voters vote directly on issues rather than representatives who make decisions on issues; basically no one thinks the US is like this, though many individual states in the US incorporate some degree of direct democracy via initiative and referendum.

I think it would be more accurate than your formulation to say "We are a federal republic with a very loose approximation of representative democracy, but most people think we are, or at least should be, a representative democracy (which would still be a federal republic, but also a democratic republic.)"