* Stars are self-luminous: They generate their own light and heat through nuclear fusion.
* The Sun is a star: It absolutely fits that definition.
* "Star" can be used broadly: We often use "star" to refer to any celestial body that appears as a point of light in the night sky.
So, while the Sun is a star, it's the only star that is close enough to Earth to be the primary source of light and heat for our planet. All other stars are so far away that they appear as tiny points of light, and we don't feel their warmth.
That's why people say the Sun is the closest star, even though it's technically the *only* star in our solar system.