> A republic is a form of democracy

No, it's not.

But a democratic republic or representative democracy with republican form (as opposed to, e.g., a constitutional monarchy) is both a form of democracy and a form of republic.

There are autocratic and/or theocratic republics, among others, that are not forms of democracy.

A rebulic is a form of democracy the same way a moon is a form of planet. Instead of orbiting around the sun, it's orbiting around a planet and that planet is orbiting around the sun. Or, instead of voting directly for things, people vote for other people, that vote directly for things.