Hot matter glows according to its heat
Take a piece of iron and heat it. First it turns dark red, then orange, then yellow-white, then dazzling. The material is exactly the same; only the temperature changed - and the color traveled through a whole range. A star's surface works the same way: it is hot gas, and it glows exactly according to its heat.
A heated body does not radiate at just one wavelength, but at all of them at once - simply in different proportions. There is a wavelength that carries the maximum energy, and the hotter the surface, the shorter that maximum: it shifts from infrared to red, then yellow, blue, and into ultraviolet. Your eye blends the whole mix into one shade, and that shade is set by where the peak lies.
The peak is the color
Brightness by wavelength: the maximum determines the color
Why a blue star is hotter than a red one
In everyday life, a red mark on a faucet means "hot" and a blue one means "cold," and that habit is misleading with stars. For stars, it is the opposite. Red is a sign that the surface was not hot enough to shift the peak into short wavelengths. At about 3,000 degrees, a star is red. At 30,000 and above, it is blue. All the other colors fit between these ends.
Color says nothing about size. Red Betelgeuse is a swollen giant next to which white Sirius would look like a dot. A shade tells you only one thing: how hot the surface was that sent its light to you.
On this scale, the Sun is a relatively cool star. It seems like the benchmark of light only because it is nearby. By surface temperature, it sits in the lower third of the range, and almost every bright blue-white point in the constellations is twice as hot or more.
The Sun is about 5500 on a scale where the hottest stars have surfaces heated to 30,000 and beyond
Your eyes have a hard time with all this. You distinguish color only when there is enough brightness; when light is scarce, the part of the retina that cannot see color takes over - and stars look like white dots. Their shade shows up in the brightest ones and is more noticeable through binoculars, which collect more light. And a star's rainbow-like twinkle near the horizon is not its color, but the work of the air: it splits the beam like a prism.
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Sources
- The mechanism is thermal radiation from a heated body and Wien's displacement law: the higher the temperature, the shorter the wavelength at the peak. Surface temperatures are taken from spectral classification and rounded
- they are conventionally measured on the absolute scale, which differs from the Celsius scale by 273 degrees - at such heat, this barely changes the picture