It is believed that there are other solar systems in space. When we have our discussions about the Sun and the solar system we will be referring to the solar system which we are part of. Our Sun is a star, just like any other. The Milky Way is a spiral shaped galaxy. There is more than one galaxy in space.
Earth also belongs to the Milky Way galaxy because the Earth circles the star called the Sun.
Groups of galaxies form clusters. The Milky Way, our galaxy is only a tiny part of a grouping of galaxies called a super cluster.