Hello there.
When defining the word universe, it is when you take all of space, this is all of the matter, so the planets, moons, stars and all of the galaxies.
Space is considered an area that includes the width, depth and height and all of its dimensions. I would consider it more of a precise area of the universe.
Cosmos is a technical term, so it is used as a synonym of universe. Cosmo is Greek and means World or Universe.