Why are some stars red and others blue-white?

Look closely at the night sky and the stars aren't all the same white. Some glow a warm orange-red, like Betelgeuse in Orion; others burn a cool, icy blue-white, like Rigel nearby. But here's the twist: in everyday life we call red "hot" and blue "cold," yet with stars it's the other way round. So what is a star's colour really telling us?