Well, first off, the Sun is a star like the billions upon billions of other stars in the Milky Way galaxy that we live in. By the way, the Milky Way galaxy is only one of almost a Trillion other GALAXIES!
In fact the Sun appears different only because it is so close to us.
The light the Sun emits at its surface (photosphere actually since the Sun does NOT have a surface you could stand on) takes 8 minutes to reach us travelling at the speed of light. The NEXT nearest star to Earth is called Proxima Centauri and light from THAT star takes four years to reach us!
Now many of the stars you can see on a clear night all night long (the circumpolar stars of our latitude) are still “out there” during the day. You can’t see them because the Sun is so bright. It would be like you facing a car at night with its HIGH BEAMS on shining right in your face. Now, if someone siting in the car in addition shined a flashlight towards you, you would not be able to realize that… the high beam auto lights would make that impossible!
The Sun actually is fixed in the sky and its motion across OUR sky is called apparent motion. That is the Sun sets each day because the Earth is spinning and the spin carries everyone into the sun at local dawn and away from the sun at local sunset. Just do a simple experiment:
Take a ball and have a friend stand away from you and rotate the ball on its up/down axis while you shine a flashlight at the globe. At any given instant half the globe is getting light and the other have is in darkness; this is why we don’t see the Sun 24/7.
However, now imagine a star that is far, far away and sits along the projection of the Earth spin axis… then that star will never set or use since the spin of the Earth will never block its light from reaching us. A good example is the North Star, a star called Polaris.
Now you should make the following observation TONIGHT after dark if it is clear: Go outside and point yourself towards the North (use a compass or your iPhone!) Then look up about 35 degrees above the North Horizon. You should be able to spot the North Star.