Asteroids are chunks of rock that orbit the Sun in a belt. They are not very big though, if they were all put together, they would form a body no more than 1500km in diameter! The biggest asteroid in the Asteroid Belt is Ceres, and it is only around 900km across, another asteroid, called Braille, is only 2km in diameter!
Asteroids don't get very bright either. The brightest ones only get to around magnitude 6 or 7. You need a telescope or a pair of binoculars to be able to see any.
Comets are a bit different from asteroids. They orbit in big, elliptical orbits. Some go out to the edge of the Solar System and then back into the inner Solar System, but others can go way out of the Solar System, past the orbit of Pluto! As they come back into the inner Solar System, and get closer to the Sun, they get brighter and brighter. Some of them get bright enough to be visible with the naked eye. As they get closer to the Sun, they also start to form a tail.
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