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How does the universe differ from what? We only know of the one, so it's hard to imagine what we could compare it to.
If you mean how do these things differ from each other... pretty much completely.
A planet is a celestial body that isn't a star, is large enough to have its own weight pull it into hydrostatic equilibrium (you can basically think of this as "being round"), and has "cleared its orbit", which is a little complicated but basically means that it's the biggest thing anywhere near its own orbit by a large margin (some exceptions could be made for "double planets", where two similarly-sized objects share the same orbit and also orbit each other).
A solar system consists of at least one star and at least one other object, which could be another star or a planet or even just gravitationally bound debris (like asteroids or comets).
The universe is everything. Which is why we only know of the one, there's only one set of "everything". It's possible to quibble about this and talk about parallel universes or alternate universes which are separate from ours in some way, but we don't know of any and probably can't know of any.
There is only one Solar System, which consists of our Sun and all the objects that orbit it, including planets, moons, asteroids, and comets.
We do not know. Although we have detected planets in other solar systems, we do not know what colors they are.
Since a galaxy can have many solar systems and a solar system might have more than one planet, for each galaxy there would be many planets. Therefore there would be more planets than galaxies.
Our own galaxy has between 100 and 400 billion stars; there are hundreds of billions of similar galaxies in the OBSERVABLE Universe, and it is believed that the entire Universe is much, much bigger than the observable Universe (how much bigger, is not known). It seems that at least a large percentage of those stars have planets, which means they can be called "solar systems".
The distance between planets are measured in millions of kilometers while the distance between solar systems are measured in light years while the galxies and the universe are measured in AU (astronautical units)