why do we classify the sun as a star?
The sun undergoes nuclear fusion within its core, which is something stars do and planets don't do. Not only is the sun a star, but it's actually the closest star to Earth and vital for life here. Our sun appears to be yellow from our viewpoint here on Earth, but it is actually white!
In the 1800s a technique called spectroscopy was used to analyse the Sun. When light is slipt into the full spectrum of colours, dark bands can be seen which correspond to chemical elements. It's like a signature. When the same technique was used to analyse the light from stars, the same patterns of lines appeared. In other words, the Sun and the stars were made of the same stuff. We only think of the Sun as different because we are so much closer to it.