A republic is a type of democracy. It just means you also have constitution and elected representatives rather than direct democracy, which is also a type of democracy.
No, a Republic is not a form of Democracy, it is a Republic. We are a Democratic Republic. Two different systems, but somewhat combined.
No, the essential difference is that a Republic has a separation of powers.
The Roman Republic executive was ruled not by one president, but by TWO consuls. Many other executive jobs were like that, divided power. The Roman Republic had a complex legislature, something like four houses. It wasn't just the Senate.
Now compare that to Democracy where only the most recent election matters. That's the key difference, in a Democracy it only takes a single election win to grab control of all the levers of power. In a Republic there are multiple institutions and no single election can mess things up.
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