Comets and asteroids are similar in that both are the remains of the creation of the universe around 4.5 billion years ago, and both can move toward Earth. That is where their similarities end.
A comet is a ball made of ice and rock that grows "tails" as it gets closer to the sun. The tails are formed as the comet moves, picking up gas, dust and other debris that trails behind it. An asteroid is a ball of rock that, together with other asteroids, orbit the sun in what is called an asteroid belt.
Most asteroids are too small to cause any real damage to Earth. When an asteroid burns up in Earth's atmosphere, it may be seen by humans as a shooting star.