greenhronet,
the USA is both a republic and a democracy. We are a republic in that we have an elected President instead of a hereditary monarch or any other kind of monarch. We are a democracy, in the form of a representative democracy. Also to some extent we are a direct/pure democracy since the people, in at at least states, have the opportunity to vote directly on some legislation (and even to write such legislation) in the form of Initiative Ballot Measures. Furthermore, one definition (found in dictionaries) of the word "republic" is "a representative democracy".
https://en.wikipedia.org/wiki/Democratic_republic (quote definitions from the definitions from the Oxford English Dictionary ) says "Democracy: "A system of government by the whole population or all
the eligible members of a state, typically through elected
representatives." Though the original form of democracy was not "through elected
representatives", modern ones (at least the vast majority of them) are.
The Wikipedia article also says the following.
"Eugene Volokh of the UCLA School of Law notes that the United States
exemplifies the varied nature of a constitutional republic—a country
where some decisions (often local) are made by direct democratic
processes, while others (often federal) are made by democratically
elected representatives.[3]
As with many large systems, US governance is incompletely described by
any single term. It also employs the concept, for instance, of a constitutional democracy in which a court system is involved in matters of jurisprudence.[3] "
It has been my observation that people who say the USA is "a republic not a democracy" are people who are members of the Republican Party or who align with it, but not with the Democratic Party. In contrast I have never heard (nor read) any Democrat or anyone else say the USA is "a democracy not a republic", though Democrats more commonly say the USA "is a democracy" than they say it "is a republic". To me the USA is a democratic republic.