Either I didn't get your question, or you're a bit confused about the structure of the universe. Not a problem.
There's Earth, it's a planet orbiting our star, Sol AKA the Sun, in our solar system. A star has plenty of bodies orbiting around it, dust, asteroids, planets, so the whole group is called a solar system.
There's other stars "next" to us, which in turn have dust, asteroids and planets orbiting around them. So they also are solar systems, since all stars have stuff orbiting around them.
Stars (/solar systems) tend to cluster together in a galaxy. A galaxy is composed of billions of stars.
Earth/our Solar system is in the Milky Way galaxy, so most of the stuff we see in the sky are stars that are not very far from us and/or part of the Milky Way galaxy.
The closest galaxy from ours is Andromeda, which is in turn composed of billions of stars, and countless planets.
So, the order is planet (Earth) -> star (Sun) -> (grouped into a) solar system -> galaxy (Milky Way)
Binary systems are solar systems which do not have a single star, but they have TWO! and these stars orbit each other. A galaxy has millions of binary systems (not sure how rare they are)
Uranus, Neptune, etc. are part of our solar system, so yeah, the stars you see are farther beyond.
EDIT: apparently I'm a bit confused as well, as star/planet groups are called planetary systems, and only ours is called the Solar System (from Sol/the Sun). The more you know.
Note that the Magellanic Clouds are basically orbiting our galaxy, and that the next closest independent galaxy is Andromeda, 2 and a half million light years away.
There's Earth, it's a planet orbiting our star, Sol AKA the Sun, in our solar system. A star has plenty of bodies orbiting around it, dust, asteroids, planets, so the whole group is called a solar system.
There's other stars "next" to us, which in turn have dust, asteroids and planets orbiting around them. So they also are solar systems, since all stars have stuff orbiting around them.
Stars (/solar systems) tend to cluster together in a galaxy. A galaxy is composed of billions of stars.
Earth/our Solar system is in the Milky Way galaxy, so most of the stuff we see in the sky are stars that are not very far from us and/or part of the Milky Way galaxy.
The closest galaxy from ours is Andromeda, which is in turn composed of billions of stars, and countless planets.
So, the order is planet (Earth) -> star (Sun) -> (grouped into a) solar system -> galaxy (Milky Way)
Binary systems are solar systems which do not have a single star, but they have TWO! and these stars orbit each other. A galaxy has millions of binary systems (not sure how rare they are)
Uranus, Neptune, etc. are part of our solar system, so yeah, the stars you see are farther beyond.
EDIT: apparently I'm a bit confused as well, as star/planet groups are called planetary systems, and only ours is called the Solar System (from Sol/the Sun). The more you know.
Does this help and answer your question?