Final answer:
Short-period comets typically originate in the Kuiper Belt, while long-period comets come from the Oort Cloud, with these regions housing icy bodies that sometimes enter the inner solar system as comets.
Step-by-step explanation:
Short-period comets exist primarily in the Kuiper Belt; while long-period comets are typically found in the Oort Cloud. The Kuiper Belt is a disk-shaped region that extends beyond the orbit of Neptune, roughly to 50 AU from the Sun, and includes ice-and-rock planetesimals that are remnants of the early solar system. The Oort Cloud, on the other hand, is a distant, spherical reservoir of icy bodies that surrounds the Sun out to about 50,000 AU, almost a light-year away, containing trillions of comet-like objects. Objects from these regions have different histories and compositions, and when they are diverted into the inner solar system, they can become visible as comets. Short-period comets often come from the Kuiper Belt, where they're influenced by small gravitational perturbations, whereas long-period comets hail from the distant Oort Cloud, their orbits influenced sometimes by the gravity of passing stars.