A septic tank is one component of a subsurface disposal (septic) system. It is usually the first stop for raw sewage as it leaves the building or dwelling, it's a baffled tank of usually 700-1500 gallons. It's job is to start the process of breaking down the solids that are sent into the system. Bacteria in the tank "digest" most of the solids, but what they can't eat falls to the bottom of the tank, which is why you should get your septic tank pumped out occasionally, typically 1-2 years. The liquid then leaves the tanks as Effluent, it travels to some sort of a leaching system either by gravity or a pump. The leaching system (pipes in a stone bed, chambers, trenches, etc) slowly allows the liquid to percolate back into the groundwater, but there is another stage of bacteria that process the liquid and remove more impurities.
A cesspool is all-in-one, a basic tank that accepts all the raw sewage. Most have perforations in the bottom so the liquid eventually percolates into the groundwater table, although a sealed cesspool (also called a "holding tank") has to be pumped out whenever it is full.
If there is no outlet pipe from the tank, then it's a cesspool. If there is a pipe coming out of it that leads to some sort of leaching system, then it's a septic tank.
Most states no longer allow cesspools to be installed.
