Everything you see is part of the Universe. Everything. Everything on Earth and everything you can observe in the sky is all part of the Universe. Even objects we cannot observe are part of the Universe, which is why astronomers often distinguish between the Universe and the observable Universe.
Space is often used to refer to that part of the universe between planets or stars or galaxies. It is used when there is a lack of matter present. Above Earth's atmosphere, there are very few atoms around, which is why we can't breathe in space—there's no air particles (atoms and molecules) to breathe in.
In reality, atoms, or matter, exist everywhere in the universe, but between planets, stars or galaxies there are relatively few of them compared with the 1050 atoms on Earth.
