Are all stars on the same horizontal plane?

Answer 1

No, not if you think of horizontal plane in the strict geometric sense of plane. If that were true, we would see all the stars in a straight line only, with blackness everywhere else. You are probably thinking about what you are learning regarding the Milky Way. Yes, in Universal terms it is a big, relatively thin and flat swirling disc of stars with a super-massive black hole in its center. But 'thin and flat' in universal terms doesn't quite mean that we would 'see' the galaxy from earth as if it's a well-made crepe. Even though we are out in one of Milky Way's arms, the view from earth is mostly cloud-like. If you are fortunate enough to live where the night sky is not hopelessly polluted with light, you have seen the broad, cloudy path through the sky that inspires the Milky Way's name. You are actually seeing the 'width' of the galaxy where the stars are more dense. The rest of the stars in the sky are stars that are closer to us in the cloudy bulk of this part of the galaxy. We do see some other galaxies with the naked eye as well, but not that many; most are much too far away to see with the naked eye.

Speaking of crepes, imagine yourself now living on a single atom in the center of the thickness of a crepe. Is your 'galaxy' a relatively flat and thin disc? Well, yes... but you'll see nothing but other atoms all around you, just the same.

Answer 2

From our position on the Earth's surface, the physical distance between stars we view in any given constellation can vary greatly. Some stars aren't even stars, but other galaxies.