No, two stars with the same apparent magnitude are not necessarily the same distance from Earth.

Here's why:

* Apparent magnitude is how bright a star appears to us on Earth. It's influenced by both the star's intrinsic brightness (luminosity) and its distance from us.

* Luminosity is the actual amount of light a star emits.

Think of it like this: Imagine two lightbulbs. One is a dim bulb close to you, and the other is a very bright bulb far away. They could appear to have the same brightness to your eye, even though they're very different in their actual light output and distance from you.

Here are some examples:

* A nearby, dim star could have the same apparent magnitude as a distant, bright star.

* Two stars of the same luminosity could have different apparent magnitudes if they are at different distances from us.

In summary: Apparent magnitude is just a measure of how bright a star appears from Earth, not its actual brightness or distance.