This is a very simple one but many people can’t draw the distinction.
A republic is an alternative to a monarchy. Where we have the Queen, a republic could have a Directory, a Council, or a President.
A democracy is simply a state that allows people to vote. You can be nominally democratic – like China or North Korea – or an actual democracy, like the UK or Germany.
So the UK is not a republic, and is a democracy, Germany is a republic and is a democracy, China is a republic but is not a democracy, and Saudi Arabia is not a republic and is not a democracy.