A federal republic is a type of democracy. Often those that make this hard distinction are thinking republic vs direct democracy, which while accurate doesn’t capture the democracy most people are referring to when they say the US is a democracy. They mean the US is a modern liberal democracy, which it is, and has the constitutional federal republic style of government. I point this out not to nitpick, but because the right has used the argument that the US isn’t a democracy to justify eroding our rights.