A Democratic Republic is a form of Democracy, as opposed to a form of Dictatorship or Hereditary or Military rule, or a Theocracy.
Other forms of Democracy are Palimentary and Direct. Our Republican form is better, but it's still a Democracy.
People who beat up on other posters when they say we are a Democracy are incorrect, in my opinion, or playing silly word games.
For the time being, we are a republic. Period.