There's a bit of a misconception here. The two brightest "stars" you see near the moon are actually planets, not stars. They are:

* Venus: Often the brightest object in the night sky after the moon, Venus is known as the "Evening Star" or "Morning Star" depending on its position relative to the sun.

* Jupiter: The largest planet in our solar system, Jupiter is a gas giant and often appears as a bright, white "star".

While stars are much larger than planets, they are also much farther away. This makes them appear much smaller and fainter than planets in our own solar system.