Comets have highly elliptical orbits, with the Sun at one focus. When they come in close to the Sun they speed up, due to the larger gravitational force on them. They also develop bright tails that point away from the centre of the Sun. These are caused by tiny ice crystals that melt and break off from the comet and reflect the bright light of the Sun.
Moons have circular orbits and planets orbit in slightly squashed circles, called ellipses.