Bingo! Exactly correct. There are many forms of democracy. A republic is just one kind of democracy.
Continuing with an analogy . . . We wouldn't say an oak is not a tree because it's an oak. An oak is a tree. Similarly, America is a democracy, but it's a special species of democracy called a republic.
The government that was chosen and set forth in the founding documents which are the law of this land is a republic. It is NOT a form of democracy. In a republic, individual rights are the final word; in a democracy, 49% of the people are at the mercy of 51% of the rest of the people. There are no individual rights, only group “rights”. This group historically destroys their democracy because they vote for more and more “freebies” until there’s nothing left. It becomes mob rule at some point.