Sure. That's how I understand the English Wikipedia. There are other types of stars in my native tongue at least. But as far as I understand, they are the same in English.

So give me your counter example

Sun and Star are synonyms.

Here is the first sentence of the Wikipedia article for :

The Sun is the star at the center of the Solar System.

Here are the first two sentences for :

A star is an astronomical object comprising a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun.