Here in New England many towns do not have public sewer systems, so homeowners have either a septic system or a cesspool. What is the difference between the two?
Septic systems leach out into the surrounding area (called a "leach field"). This helps reduce the number of times the system needs pumped out. Liquid (and some solid) waste is broken down and leaches out into the field. Some municipalities don't like this because it has the potential to contaminate local water sheds (most notably if you're near a river).
A cesspool is a sealed tank for holding waste. Since it's sealed it doesn't leak but frequently needs drained. More expensive than a septic system but more environmentally friendly.
Most places in the US that don't have city sewer services have a septic tank as far as I'm aware. I haven't heard of many cesspools.